Question

In which directions does the function f(x; y) = 2x^2y have the rate of change 8 at the point (2; 1)?

 

I understand how to do all the steps apart from finding the direction

Answer 1

Partial differentiation Df/Dx tells us the gradient in the x direction: Df/Dx=4xy. At the point (2;1) this is 8. And similarly Df/Dy=2x^2y=8. The rate of change is +8 in each case, so the direction of the rate of change is positive in the x and y directions and has the value of 8.