Originally Posted by

**larson** Could anyone help me with this problem, which has to be done in Maple.

The temperature on a metal plate is given by T(x,y) = $\displaystyle 4x^2 - 4xy + y^2$. An ant walks around the origin along the circle of radius 5 centered at the origin. What are the highest and lowest temperatures encountered by the ant? Plot the temperature function and the points of highest and lowest temperatures together on one plot.

This is how I started it out, but I have no idea if its going in the right direction.

with(plots):

a:= (x,y) -> $\displaystyle 4x^2 - 4xy + y^2$;

b:= (x,y) -> $\displaystyle x^2 + y^2 = 25$;

display(a,b);

And right here it gives me an error saying it can't display the 2 equations.

Here's a plot of the temperature function and the circular region:

*code used to generate graph*

Code:

> with(plots):T := (x,y)-> 4*x^2+4*x*y+y^2:
> plot1 := implicitplot3d(x^2+y^2=25,x=-5..5,y=-5..5,z=0..0.001):
> plot2 := plot3d(T(x,y),x=-5..5,y=-5..5,axes=normal,labels=[x,y,z],
glossiness=0.9,transparency=0.95,lightmodel=light1,style=hidden):
> plots[display]({plot1,plot2});

--Chris