I'm hoping someone could check my work. My answers are not the same as the text gives.

The question is, "Find the maximum rate of change of f at the given point and the direction in which it occurs."

So I think the problem boils down to finding

Given and

Differentiating with respect to x and applying the chain rule;

Replacing x with y yields . Replacing x with z yields .

Since f(x,y,z) evaluated at P(3,6,-2) is 7 and I need evaluated at P I get the following expression;

evaluated at P is;

The text says the answer for this part of the question is is my answer of wrong?

Also

the text says the solution for this part of the problem is 1 so i'm pretty sure something is wrong.