Directional derivative, help

1. Feb 21, 2015

ilyas.h

1. The problem statement, all variables and given/known data
$$D_{u}(f)(a,b) = \triangledown f(a,b)\cdot u$$

$$D_{(\frac{1}{\sqrt2}, \frac{1}{\sqrt2})}(f)(a,b) = 3 \sqrt{2}$$

where $$u = (\frac{1}{\sqrt2}, \frac{1}{\sqrt2})$$

find $$\bigtriangledown f(a.b)$$

2. Relevant equations

3. The attempt at a solution

first you change grad f into it's partial derivative form and then take the dot product:

(df/dx, df/dy).(1/root2, 1/root2) = 3root2

you'll find that:

df/dx + df/dy = 6

where would I go from here? quite confused.

2. Feb 21, 2015

Ray Vickson

There are infinitely many different gradient vectors that satisfy the given condition. You need more conditions in order to get a unique answer.

3. Feb 21, 2015

ilyas.h

so is my solution complete? if not, where would I obtain more equations to make the conditions more robust?

you could say that:

grad f(6-y, y) . (1/root2, 1/root2) = 3root2

4. Feb 21, 2015

Ray Vickson

You cannot pull more information out of the air; somebody has to give it to you. If they do not give you more information, you have gone as far as you can go.

5. Feb 21, 2015

ilyas.h

great, so df/dx + df/dy = 6 is the final solution?

sorry for bugging you, this question is quite important to me.

6. Feb 21, 2015