Let T= g(x,y) be the temperature at the point (x,y) on the ellipse x=2sqrt2 cos(t) and y= sqrt2 sin(t), t is from 0 to 2pi. suppose that partial derivative of T with respect to x is equal to y and partial derivative of T with respect to y is equal to x. Locate the max and min temperatures by examining dT/dt and the derivative of dT/dt.
chain rule with partial derivatives
The Attempt at a Solution
I got an answer of 4 for dT/dt. this means that the temperature is increasing at a constant rate of 4 units/sec. meaning that the min is at t=0 and the max at t=2pi. do i need to find the area under the dT/dt graph to find the max and min temps? or am i way off?