The Gradient direction and rate of maximum increase

[DrunkApple]

Homework Statement

What is the direction and rate of maximum increase?
f(x,y) = x^2 + y^3, v = <4,3>, P = (1,2)

Homework Equations

The Attempt at a Solution

The direction should be as same as the gradient so < 2,12>
The rate of maximum increase is magnitude of the gradient so sqrt(4+144) = sqrt(148).
Is that right?

 

[LCKurtz]

Yes.