# Homework Help: Direction of maximum increase and rate of change

1. Nov 17, 2011

### Hiche

1. The problem statement, all variables and given/known data

2. Relevant equations

..

3. The attempt at a solution

We find $\nabla f(1,2)$ at point P: the answer is $(-4, 13)$. Now, we know that the directional derivative of f is given by: $\nabla f(1, 2) |u| \cos\theta$
where $|u| = 1$ and $\cos\theta=1$ (since the direction is maximized at $\theta\ = 0$ or $\cos\theta=1$)
So, letting $u$ be the direction of maximum increase:

$u =$ $\frac {(-4, 13)}{\sqrt{185}}$

Is that true (for the first part)? And how can I start with the second? Any help is appreciated. Oh, and $u$ in the first part is irrelevant of the $u$ in the second part of the question.

Last edited: Nov 17, 2011