i know that the maximal growth is the gradiend of a function.

the formula is:

$\displaystyle

\triangledown f=f_x'\vec{i}+f_y'\vec{j}+f_z'\vec{k}

$

so when i am given a function

$\displaystyle f(x,y,2x^2+y^2)=3x-5y$

i am was told that it growth on point M(1,2,6) in direction $\displaystyle \hat{a}=(\frac{1}{3},\frac{2}{3},\frac{2}{3})$ is 1

what is the gradient of f (maximal growth).

i tried to get it like this:

first of all i need a function which looks like this f(x,y,z)=...

in order to find the gradient

i dont know how to do the gradient of a function which i was given.

if i substiute the point

f(1,2,6)=3-10=7

i know i should write

$\displaystyle

(grad f(1,2,6)\dot \hat{a}=1

$

????