# Directional derivative, help

## Homework Statement

$$D_{u}(f)(a,b) = \triangledown f(a,b)\cdot u$$

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

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

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

## 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.

Ray Vickson
Homework Helper
Dearly Missed

## Homework Statement

$$D_{u}(f)(a,b) = \triangledown f(a,b)\cdot u$$

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

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

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

## 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.

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

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

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

Ray Vickson
Homework Helper
Dearly Missed
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-b, b) . (1/root2, 1/root2) = 3root2

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.

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.

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

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

Ray Vickson