A first look at Tangent Planes Worksheet by Mike May, S.J.- maymk@slu.edu restart: with(plots): A first naive way to look at tangent planes is to take the tangent lines to the two cross section curves at a point and turn those lines into a plane. (The naive approach works if the function is differentiable, but that is a detail we will look at later.) An earlier worksheet looked at a demonstrtion of that technique. This worksheet converts to a component style for use with MapleNet. Throughout the worksheet closed text sections describe how to create the compoenets with the appropriate coding.

We start by defining a function that we will work with. Our favorite function is z=f(x,y) =x^2-3*x*y+y^2. We would like to specify a range and look at a graph with a specified range f(x, y)=use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # GetProperty( component_name, attribute_name ) # and # SetProperty( component_name, attribute_name, value ) # to access any of the attributes of the component. # See ?CustomizingComponents for more information. f1 := parse(GetProperty(TextFunction,'value')); r1 := parse(GetProperty(TextXRange,'value')); r2 := parse(GetProperty(TextYRange,'value')); SetProperty(Plotf, 'value', plot3d(f1, x=r1,y=r2, axes=boxed)); end use; xRange=use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # GetProperty( component_name, attribute_name ) # and # SetProperty( component_name, attribute_name, value ) # to access any of the attributes of the component. # See ?CustomizingComponents for more information. f1 := parse(GetProperty(TextFunction,'value')); r1 := parse(GetProperty(TextXRange,'value')); r2 := parse(GetProperty(TextYRange,'value')); SetProperty(Plotf, 'value', plot3d(f1, x=r1,y=r2, axes=boxed)); end use; , yRange=use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # GetProperty( component_name, attribute_name ) # and # SetProperty( component_name, attribute_name, value ) # to access any of the attributes of the component. # See ?CustomizingComponents for more information. f1 := parse(GetProperty(TextFunction,'value')); r1 := parse(GetProperty(TextXRange,'value')); r2 := parse(GetProperty(TextYRange,'value')); SetProperty(Plotf, 'value', plot3d(f1, x=r1,y=r2, axes=boxed)); end use; use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # GetProperty( component_name, attribute_name ) # and # SetProperty( component_name, attribute_name, value ) # to access any of the attributes of the component. # See ?CustomizingComponents for more information. f1 := parse(GetProperty(TextFunction,'value')); r1 := parse(GetProperty(TextXRange,'value')); r2 := parse(GetProperty(TextYRange,'value')); SetProperty(Plotf, 'value', plot3d(f1, x=r1,y=r2, axes=boxed)); end use; 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To give some breakdown of how this is done: 1) A set of boxes, a button, and a graph was added to the worksheet from the components pallette. Each was editted with the Component Properties selection form the edit menu. They were given names TextFunction, TextXRange, TextYRange, Plotf, ButtonUpdate. The text boxes were given appropriate default values. 2) The following block of code was tested in an execution block use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # GetProperty( component_name, attribute_name ) # and # SetProperty( component_name, attribute_name, value ) # to access any of the attributes of the component. # See ?CustomizingComponents for more information. f1 := parse(GetProperty(TextFunction,'value')); r1 := parse(GetProperty(TextXRange,'value')); r2 := parse(GetProperty(TextYRange,'value')); SetProperty(Plotf, 'value', plot3d(f1, x=r1,y=r2, axes=boxed)); end use; 3) Each componet was opened again and the same block of code was entered into the component, either under an edit button, or under action on change.

Notice that the graph is a paraboloid. To find the tangent plane we considered cross sections through a base point. We will start with the base point being (-1,2). x0=, y0= We compute the value of the z coordinate, the slice curves (funtions in one variable obtained by evaluating the other variable at a constant), the derivatives of the slice curves, and the slopes of those curves. use DocumentTools in # Enter Maple commands to be executed when the specified # Use: # GetProperty( component_name, attribute_name ) # and # SetProperty( component_name, attribute_name, value ) # to access any of the attributes of the component. # See ?CustomizingComponents for more information. # See ?CustomizingComponents for more information. f := parse(GetProperty(TextFunction,'value')): x0 := parse(GetProperty(TextX0,'value')): y0 := parse(GetProperty(TextY0,'value')): z0 := eval(f,{x=x0,y=y0}): SetProperty(TextZ0, 'value', z0): fy0 := eval(f,(y=y0)): SetProperty(TextFy0, 'value', fy0): fy0x := diff(fy0,x); SetProperty(TextDfy0, 'value', fy0x): mx := eval(fy0x,x=x0); SetProperty(Textmx, 'value', mx): fx0 := eval(f,(x=x0)): SetProperty(TextFx0, 'value', fx0): fx0y := diff(fx0,y); SetProperty(TextDfx0, 'value', fx0y): my := eval(fx0y,y=y0); SetProperty(Textmy, 'value', my): end use;

For the next set up we have a number of new test boxes controlled by the button ButtonComputations. The input text areas remain TextFunction, TextX0, and TextY0. the output test areas are TextZ0, TextFy0, TextFx0, TextDfy0, TextDfx0, Textmx, and Textmy. The section of commands in the button unit is: use DocumentTools in # Enter Maple commands to be executed when the specified # Use: # GetProperty( component_name, attribute_name ) # and # SetProperty( component_name, attribute_name, value ) # to access any of the attributes of the component. # See ?CustomizingComponents for more information. # See ?CustomizingComponents for more information. f := parse(GetProperty(TextFunction,'value')): x0 := parse(GetProperty(TextX0,'value')): y0 := parse(GetProperty(TextY0,'value')): z0 := eval(f,{x=x0,y=y0}): SetProperty(TextZ0, 'value', z0): fy0 := eval(f,(y=y0)): SetProperty(TextFy0, 'value', fy0): fy0x := diff(fy0,x); SetProperty(TextDfy0, 'value', fy0x): mx := eval(fy0x,x=x0); SetProperty(Textmx, 'value', mx): fx0 := eval(f,(x=x0)): SetProperty(TextFx0, 'value', fx0): fx0y := diff(fx0,y); SetProperty(TextDfx0, 'value', fx0y): my := eval(fx0y,y=y0); SetProperty(Textmy, 'value', my): end use;

z0=. fy0(x)=, fx0(y)= . Dfy0(x)=, Dfy0(x)=. mx=, my= We see that the x slope is -6, the y-slope is 13, and the z value is 16. We are now ready to plot. We also want a range for z. zRange=use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # GetProperty( component_name, attribute_name ) # and # SetProperty( component_name, attribute_name, value ) # to access any of the attributes of the component. # See ?CustomizingComponents for more information. end use; use DocumentTools in # Enter Maple commands to be executed when the specified # Use: # GetProperty( component_name, attribute_name ) # and # SetProperty( component_name, attribute_name, value ) # to access any of the attributes of the component. # See ?CustomizingComponents for more information. # See ?CustomizingComponents for more information. with(plots): f := parse(GetProperty(TextFunction,'value')): range1 := parse(GetProperty(TextXRange,'value')); range2 := parse(GetProperty(TextYRange,'value')); range3 := parse(GetProperty(TextZRange,'value')); x0 := parse(GetProperty(TextX0,'value')): y0 := parse(GetProperty(TextY0,'value')): z0 := parse(GetProperty(TextZ0,'value')): fy0 := parse(GetProperty(TextFy0,'value')): mx := parse(GetProperty(Textmx,'value')): fx0 := parse(GetProperty(TextFx0,'value')): my := parse(GetProperty(Textmy,'value')): tanplane := z0+mx*(x-x0)+my*(y-y0); surfaces := plot3d([f, tanplane], x = range1, y = range2, view = range3, color = ([blue, red])): xCurve := spacecurve([x, y0, fy0], x = range1, color = green, thickness = 3): yCurve := spacecurve([x0, y, fx0], y = range2, color = yellow, thickness = 3): xTanLine := spacecurve([x, y0, z0+mx*(x-x0)], x = range1, color = green, thickness = 2): yTanLine := spacecurve([x0, y, z0+my*(y-y0)], y=range2, color = yellow, thickness = 2): SetProperty(Plot2f, 'value', display3d({yCurve, surfaces, xCurve, xTanLine, yTanLine}, axes = boxed)); end use;

The commands under the plot button are: use DocumentTools in # Enter Maple commands to be executed when the specified # Use: # GetProperty( component_name, attribute_name ) # and # SetProperty( component_name, attribute_name, value ) # to access any of the attributes of the component. # See ?CustomizingComponents for more information. # See ?CustomizingComponents for more information. with(plots): f := parse(GetProperty(TextFunction,'value')): range1 := parse(GetProperty(TextXRange,'value')); range2 := parse(GetProperty(TextYRange,'value')); range3 := parse(GetProperty(TextZRange,'value')); x0 := parse(GetProperty(TextX0,'value')): y0 := parse(GetProperty(TextY0,'value')): z0 := parse(GetProperty(TextZ0,'value')): fy0 := parse(GetProperty(TextFy0,'value')): mx := parse(GetProperty(Textmx,'value')): fx0 := parse(GetProperty(TextFx0,'value')): my := parse(GetProperty(Textmy,'value')): tanplane := z0+mx*(x-x0)+my*(y-y0); surfaces := plot3d([f, tanplane], x = range1, y = range2, view = range3, color = ([blue, red])): xCurve := spacecurve([x, y0, fy0], x = range1, color = green, thickness = 3): yCurve := spacecurve([x0, y, fx0], y = range2, color = yellow, thickness = 3): xTanLine := spacecurve([x, y0, z0+mx*(x-x0)], x = range1, color = green, thickness = 2): yTanLine := spacecurve([x0, y, z0+my*(y-y0)], y=range2, color = yellow, thickness = 2): SetProperty(Plot2f, 'value', display3d({yCurve, surfaces, xCurve, xTanLine, yTanLine}, axes = boxed)); end use;

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Thus we see that we have constructed a point that contains the appropriate point of the surface and contains the two tangent lines.

f(x, y)=use DocumentTools in # Enter Maple commands to be executed when the specified # Use: # GetProperty( component_name, attribute_name ) # and # SetProperty( component_name, attribute_name, value ) # to access any of the attributes of the component. # See ?CustomizingComponents for more information. # See ?CustomizingComponents for more information. with(plots): f := parse(GetProperty(TextFunction2,'value')): range1 := parse(GetProperty(TextXRange2,'value')); range2 := parse(GetProperty(TextYRange2,'value')); range3 := parse(GetProperty(TextZRange2,'value')); x0 := parse(GetProperty(TextX02,'value')): y0 := parse(GetProperty(TextY02,'value')): z0 := eval(f,{x=x0,y=y0}): fy0 := eval(f,y=y0): SetProperty(MathContainerFy0, 'value', fy0); Dfy0 := diff(fy0,x): SetProperty(MathContainerDfy0, 'value', Dfy0); mx := eval(Dfy0,x=x0): SetProperty(MathContainermx, 'value', mx); fx0 := eval(f,{x=x0}): SetProperty(MathContainerFx0, 'value', fx0); Dfx0 := diff(fx0,y): SetProperty(MathContainerDfx0, 'value', Dfx0); my := eval(Dfx0,y=y0): SetProperty(MathContainermy, 'value', my); tanplane := z0+mx*(x-x0)+my*(y-y0); surfaces := plot3d([f, tanplane], x = range1, y = range2, view = range3, color = ([blue, red])): xCurve := spacecurve([x, y0, fy0], x = range1, color = green, thickness = 3): yCurve := spacecurve([x0, y, fx0], y = range2, color = yellow, thickness = 3): xTanLine := spacecurve([x, y0, z0+mx*(x-x0)], x = range1, color = green, thickness = 2): yTanLine := spacecurve([x0, y, z0+my*(y-y0)], y=range2, color = yellow, thickness = 2): SetProperty(Plot3f, 'value', display3d({yCurve, surfaces, xCurve, xTanLine, yTanLine}, axes = boxed)); end use; xRange=use DocumentTools in # Enter Maple commands to be executed when the specified # Use: # GetProperty( component_name, attribute_name ) # and # SetProperty( component_name, attribute_name, value ) # to access any of the attributes of the component. # See ?CustomizingComponents for more information. # See ?CustomizingComponents for more information. with(plots): f := parse(GetProperty(TextFunction2,'value')): range1 := parse(GetProperty(TextXRange2,'value')); range2 := parse(GetProperty(TextYRange2,'value')); range3 := parse(GetProperty(TextZRange2,'value')); x0 := parse(GetProperty(TextX02,'value')): y0 := parse(GetProperty(TextY02,'value')): z0 := eval(f,{x=x0,y=y0}): fy0 := eval(f,y=y0): SetProperty(MathContainerFy0, 'value', fy0); Dfy0 := diff(fy0,x): SetProperty(MathContainerDfy0, 'value', Dfy0); mx := eval(Dfy0,x=x0): SetProperty(MathContainermx, 'value', mx); fx0 := eval(f,{x=x0}): SetProperty(MathContainerFx0, 'value', fx0); Dfx0 := diff(fx0,y): SetProperty(MathContainerDfx0, 'value', Dfx0); my := eval(Dfx0,y=y0): SetProperty(MathContainermy, 'value', my); tanplane := z0+mx*(x-x0)+my*(y-y0); surfaces := plot3d([f, tanplane], x = range1, y = range2, view = range3, color = ([blue, red])): xCurve := spacecurve([x, y0, fy0], x = range1, color = green, thickness = 3): yCurve := spacecurve([x0, y, fx0], y = range2, color = yellow, thickness = 3): xTanLine := spacecurve([x, y0, z0+mx*(x-x0)], x = range1, color = green, thickness = 2): yTanLine := spacecurve([x0, y, z0+my*(y-y0)], y=range2, color = yellow, thickness = 2): SetProperty(Plot3f, 'value', display3d({yCurve, surfaces, xCurve, xTanLine, yTanLine}, axes = boxed)); end use; , yRange=use DocumentTools in # Enter Maple commands to be executed when the specified # Use: # GetProperty( component_name, attribute_name ) # and # SetProperty( component_name, attribute_name, value ) # to access any of the attributes of the component. # See ?CustomizingComponents for more information. # See ?CustomizingComponents for more information. with(plots): f := parse(GetProperty(TextFunction2,'value')): range1 := parse(GetProperty(TextXRange2,'value')); range2 := parse(GetProperty(TextYRange2,'value')); range3 := parse(GetProperty(TextZRange2,'value')); x0 := parse(GetProperty(TextX02,'value')): y0 := parse(GetProperty(TextY02,'value')): z0 := eval(f,{x=x0,y=y0}): fy0 := eval(f,y=y0): SetProperty(MathContainerFy0, 'value', fy0); Dfy0 := diff(fy0,x): SetProperty(MathContainerDfy0, 'value', Dfy0); mx := eval(Dfy0,x=x0): SetProperty(MathContainermx, 'value', mx); fx0 := eval(f,{x=x0}): SetProperty(MathContainerFx0, 'value', fx0); Dfx0 := diff(fx0,y): SetProperty(MathContainerDfx0, 'value', Dfx0); my := eval(Dfx0,y=y0): SetProperty(MathContainermy, 'value', my); tanplane := z0+mx*(x-x0)+my*(y-y0); surfaces := plot3d([f, tanplane], x = range1, y = range2, view = range3, color = ([blue, red])): xCurve := spacecurve([x, y0, fy0], x = range1, color = green, thickness = 3): yCurve := spacecurve([x0, y, fx0], y = range2, color = yellow, thickness = 3): xTanLine := spacecurve([x, y0, z0+mx*(x-x0)], x = range1, color = green, thickness = 2): yTanLine := spacecurve([x0, y, z0+my*(y-y0)], y=range2, color = yellow, thickness = 2): SetProperty(Plot3f, 'value', display3d({yCurve, surfaces, xCurve, xTanLine, yTanLine}, axes = boxed)); end use; , zRange=use DocumentTools in # Enter Maple commands to be executed when the specified # Use: # GetProperty( component_name, attribute_name ) # and # SetProperty( component_name, attribute_name, value ) # to access any of the attributes of the component. # See ?CustomizingComponents for more information. # See ?CustomizingComponents for more information. with(plots): f := parse(GetProperty(TextFunction2,'value')): range1 := parse(GetProperty(TextXRange2,'value')); range2 := parse(GetProperty(TextYRange2,'value')); range3 := parse(GetProperty(TextZRange2,'value')); x0 := parse(GetProperty(TextX02,'value')): y0 := parse(GetProperty(TextY02,'value')): z0 := eval(f,{x=x0,y=y0}): fy0 := eval(f,y=y0): SetProperty(MathContainerFy0, 'value', fy0); Dfy0 := diff(fy0,x): SetProperty(MathContainerDfy0, 'value', Dfy0); mx := eval(Dfy0,x=x0): SetProperty(MathContainermx, 'value', mx); fx0 := eval(f,{x=x0}): SetProperty(MathContainerFx0, 'value', fx0); Dfx0 := diff(fx0,y): SetProperty(MathContainerDfx0, 'value', Dfx0); my := eval(Dfx0,y=y0): SetProperty(MathContainermy, 'value', my); tanplane := z0+mx*(x-x0)+my*(y-y0); surfaces := plot3d([f, tanplane], x = range1, y = range2, view = range3, color = ([blue, red])): xCurve := spacecurve([x, y0, fy0], x = range1, color = green, thickness = 3): yCurve := spacecurve([x0, y, fx0], y = range2, color = yellow, thickness = 3): xTanLine := spacecurve([x, y0, z0+mx*(x-x0)], x = range1, color = green, thickness = 2): yTanLine := spacecurve([x0, y, z0+my*(y-y0)], y=range2, color = yellow, thickness = 2): SetProperty(Plot3f, 'value', display3d({yCurve, surfaces, xCurve, xTanLine, yTanLine}, axes = boxed)); end use; , x0=use DocumentTools in # Enter Maple commands to be executed when the specified # Use: # GetProperty( component_name, attribute_name ) # and # SetProperty( component_name, attribute_name, value ) # to access any of the attributes of the component. # See ?CustomizingComponents for more information. # See ?CustomizingComponents for more information. with(plots): f := parse(GetProperty(TextFunction2,'value')): range1 := parse(GetProperty(TextXRange2,'value')); range2 := parse(GetProperty(TextYRange2,'value')); range3 := parse(GetProperty(TextZRange2,'value')); x0 := parse(GetProperty(TextX02,'value')): y0 := parse(GetProperty(TextY02,'value')): z0 := eval(f,{x=x0,y=y0}): fy0 := eval(f,y=y0): SetProperty(MathContainerFy0, 'value', fy0); Dfy0 := diff(fy0,x): SetProperty(MathContainerDfy0, 'value', Dfy0); mx := eval(Dfy0,x=x0): SetProperty(MathContainermx, 'value', mx); fx0 := eval(f,{x=x0}): SetProperty(MathContainerFx0, 'value', fx0); Dfx0 := diff(fx0,y): SetProperty(MathContainerDfx0, 'value', Dfx0); my := eval(Dfx0,y=y0): SetProperty(MathContainermy, 'value', my); tanplane := z0+mx*(x-x0)+my*(y-y0); surfaces := plot3d([f, tanplane], x = range1, y = range2, view = range3, color = ([blue, red])): xCurve := spacecurve([x, y0, fy0], x = range1, color = green, thickness = 3): yCurve := spacecurve([x0, y, fx0], y = range2, color = yellow, thickness = 3): xTanLine := spacecurve([x, y0, z0+mx*(x-x0)], x = range1, color = green, thickness = 2): yTanLine := spacecurve([x0, y, z0+my*(y-y0)], y=range2, color = yellow, thickness = 2): SetProperty(Plot3f, 'value', display3d({yCurve, surfaces, xCurve, xTanLine, yTanLine}, axes = boxed)); end use; , y0=use DocumentTools in # Enter Maple commands to be executed when the specified # Use: # GetProperty( component_name, attribute_name ) # and # SetProperty( component_name, attribute_name, value ) # to access any of the attributes of the component. # See ?CustomizingComponents for more information. # See ?CustomizingComponents for more information. with(plots): f := parse(GetProperty(TextFunction2,'value')): range1 := parse(GetProperty(TextXRange2,'value')); range2 := parse(GetProperty(TextYRange2,'value')); range3 := parse(GetProperty(TextZRange2,'value')); x0 := parse(GetProperty(TextX02,'value')): y0 := parse(GetProperty(TextY02,'value')): z0 := eval(f,{x=x0,y=y0}): fy0 := eval(f,y=y0): SetProperty(MathContainerFy0, 'value', fy0); Dfy0 := diff(fy0,x): SetProperty(MathContainerDfy0, 'value', Dfy0); mx := eval(Dfy0,x=x0): SetProperty(MathContainermx, 'value', mx); fx0 := eval(f,{x=x0}): SetProperty(MathContainerFx0, 'value', fx0); Dfx0 := diff(fx0,y): SetProperty(MathContainerDfx0, 'value', Dfx0); my := eval(Dfx0,y=y0): SetProperty(MathContainermy, 'value', my); tanplane := z0+mx*(x-x0)+my*(y-y0); surfaces := plot3d([f, tanplane], x = range1, y = range2, view = range3, color = ([blue, red])): xCurve := spacecurve([x, y0, fy0], x = range1, color = green, thickness = 3): yCurve := spacecurve([x0, y, fx0], y = range2, color = yellow, thickness = 3): xTanLine := spacecurve([x, y0, z0+mx*(x-x0)], x = range1, color = green, thickness = 2): yTanLine := spacecurve([x0, y, z0+my*(y-y0)], y=range2, color = yellow, thickness = 2): SetProperty(Plot3f, 'value', display3d({yCurve, surfaces, xCurve, xTanLine, yTanLine}, axes = boxed)); end use; . use DocumentTools in # Enter Maple commands to be executed when the specified # Use: # GetProperty( component_name, attribute_name ) # and # SetProperty( component_name, attribute_name, value ) # to access any of the attributes of the component. # See ?CustomizingComponents for more information. # See ?CustomizingComponents for more information. with(plots): f := parse(GetProperty(TextFunction2,'value')): range1 := parse(GetProperty(TextXRange2,'value')); range2 := parse(GetProperty(TextYRange2,'value')); range3 := parse(GetProperty(TextZRange2,'value')); x0 := parse(GetProperty(TextX02,'value')): y0 := parse(GetProperty(TextY02,'value')): z0 := eval(f,{x=x0,y=y0}): fy0 := eval(f,y=y0): SetProperty(MathContainerFy0, 'value', fy0); Dfy0 := diff(fy0,x): SetProperty(MathContainerDfy0, 'value', Dfy0); mx := eval(Dfy0,x=x0): SetProperty(MathContainermx, 'value', mx); fx0 := eval(f,{x=x0}): SetProperty(MathContainerFx0, 'value', fx0); Dfx0 := diff(fx0,y): SetProperty(MathContainerDfx0, 'value', Dfx0); my := eval(Dfx0,y=y0): SetProperty(MathContainermy, 'value', my); tanplane := z0+mx*(x-x0)+my*(y-y0); surfaces := plot3d([f, tanplane], x = range1, y = range2, view = range3, color = ([blue, red])): xCurve := spacecurve([x, y0, fy0], x = range1, color = green, thickness = 3): yCurve := spacecurve([x0, y, fx0], y = range2, color = yellow, thickness = 3): xTanLine := spacecurve([x, y0, z0+mx*(x-x0)], x = range1, color = green, thickness = 2): yTanLine := spacecurve([x0, y, z0+my*(y-y0)], y=range2, color = yellow, thickness = 2): SetProperty(Plot3f, 'value', display3d({yCurve, surfaces, xCurve, xTanLine, yTanLine}, axes = boxed)); end use; f(x0,y)=, f(x,y0)= f_y(x0,y)=, f_x(x,y0)= my=, mx= 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We would now like to set up a similar setup with all the input and output gathered together

use DocumentTools in # Enter Maple commands to be executed when the specified # Use: # GetProperty( component_name, attribute_name ) # and # SetProperty( component_name, attribute_name, value ) # to access any of the attributes of the component. # See ?CustomizingComponents for more information. # See ?CustomizingComponents for more information. with(plots): f := parse(GetProperty(TextFunction2,'value')): range1 := parse(GetProperty(TextXRange2,'value')); range2 := parse(GetProperty(TextYRange2,'value')); range3 := parse(GetProperty(TextZRange2,'value')); x0 := parse(GetProperty(TextX02,'value')): y0 := parse(GetProperty(TextY02,'value')): z0 := eval(f,{x=x0,y=y0}): fy0 := eval(f,y=y0): SetProperty(MathContainerFy0, 'value', fy0); Dfy0 := diff(fy0,x): SetProperty(MathContainerDfy0, 'value', Dfy0); mx := eval(Dfy0,x=x0): SetProperty(MathContainermx, 'value', mx); fx0 := eval(f,{x=x0}): SetProperty(MathContainerFx0, 'value', fx0); Dfx0 := diff(fx0,y): SetProperty(MathContainerDfx0, 'value', Dfx0); my := eval(Dfx0,y=y0): SetProperty(MathContainermy, 'value', my); tanplane := z0+mx*(x-x0)+my*(y-y0); surfaces := plot3d([f, tanplane], x = range1, y = range2, view = range3, color = ([blue, red])): xCurve := spacecurve([x, y0, fy0], x = range1, color = green, thickness = 3): yCurve := spacecurve([x0, y, fx0], y = range2, color = yellow, thickness = 3): xTanLine := spacecurve([x, y0, z0+mx*(x-x0)], x = range1, color = green, thickness = 2): yTanLine := spacecurve([x0, y, z0+my*(y-y0)], y=range2, color = yellow, thickness = 2): SetProperty(Plot3f, 'value', display3d({yCurve, surfaces, xCurve, xTanLine, yTanLine}, axes = boxed)); end use;

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