Please help on this im a little confused.

Parametrize the upper half of the unit circle by x=cos(t),y=sin(t) , for 0 to pi.
Let T=f(x,y) be the temperature at the point (x,y) on the upper half circle.
suppose that dT/dx=10x-5y and dT/dy=-5x+10y.
Using the given parametrization and the chain rule, find the derivative dT/dt. then using single-variable calcalus, find where the minium and maximum temperatures occure.

Question

Please help on this im a little confused. 

Parametrize the upper half of the unit circle by x=cos(t),y=sin(t) , for 0 to pi.
Let T=f(x,y) be the temperature at the point (x,y) on the upper half circle. 
suppose that dT/dx=10x-5y  and dT/dy=-5x+10y.
Using the given parametrization and the chain rule, find the derivative dT/dt. then using single-variable calcalus, find where the minium and maximum temperatures occure.

anonymous · Answer

i dont remember but maybe use polar coordinants?

anonymous · Answer

umm im not sure i emailed my professor and got this as a response
"This is basically a one variable max/min problem, but the function you're studying is the composition of a function f(x,y) with a parametric curve ((x(t),y(t)). So the function is just g(t) = f(x(t),y(t)). To find max/min, solve g'(t) = 0 as in calc 1."