Directional derivative, help

  • Thread starter ilyas.h
  • Start date
  • #1
60
0

Homework Statement


[tex]D_{u}(f)(a,b) = \triangledown f(a,b)\cdot u[/tex]

[tex]D_{(\frac{1}{\sqrt2}, \frac{1}{\sqrt2})}(f)(a,b) = 3 \sqrt{2}[/tex]

where [tex]u = (\frac{1}{\sqrt2}, \frac{1}{\sqrt2})[/tex]

find [tex]\bigtriangledown f(a.b)[/tex]

Homework Equations




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.
 

Answers and Replies

  • #2
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,722

Homework Statement


[tex]D_{u}(f)(a,b) = \triangledown f(a,b)\cdot u[/tex]

[tex]D_{(\frac{1}{\sqrt2}, \frac{1}{\sqrt2})}(f)(a,b) = 3 \sqrt{2}[/tex]

where [tex]u = (\frac{1}{\sqrt2}, \frac{1}{\sqrt2})[/tex]

find [tex]\bigtriangledown f(a.b)[/tex]

Homework Equations




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.
 
  • #3
60
0
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
 
  • #4
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,722
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.
 
  • #5
60
0
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.
 
  • #6
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,722
great, so df/dx + df/dy = 6 is the final solution?

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

Asked and answered.
 

Related Threads on Directional derivative, help

Replies
2
Views
515
Replies
2
Views
2K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
2
Views
4K
  • Last Post
Replies
9
Views
573
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
726
Top