# 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