Replacing x with y yields $\displaystyle f_y$. Replacing x with z yields $\displaystyle f_z$.

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

$\displaystyle \vec\nabla f=<(7)^{\frac{-1}{2}}*x,(7)^{\frac{-1}{2}}*y,(7)^{\frac{-1}{2}}*z>$

$\displaystyle \vec\nabla f$ evaluated at P is;

$\displaystyle \vec\nabla f=<(7)^{\frac{-1}{2}}*3,(7)^{\frac{-1}{2}}*6,(7)^{\frac{-1}{2}}*-2>=\frac{1}{\sqrt7}<3,6,-2>$

The text says the answer for this part of the question is $\displaystyle <3,6,-2>$ is my answer of $\displaystyle \frac{1}{\sqrt7}<3,6,-2>$wrong?

Also

$\displaystyle \|\vec\nabla f\|=\sqrt{ \frac{9}{7} + \frac{36}{7}+\frac{4}{7}}=\sqrt{\frac{49}{7}}$

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