Need help with gradient question.

[ozone]

Homework Statement

I have been able to solve all the gradient problems when you are given the starting point, and the actual function. But I am getting caught up on this one which goes in reverseSuppose that the maximum rate of change of f at (1,-1) is 25 and it occurs in the direction of 3i ⃗-4j ⃗

b) Find ∇f at (1,-1). c) Find $f_x$(1,-1). d) Find $f_y (1,-1)$.

Homework Equations

Well I know that $∇f* u = |∇f|$
and I think we know that $f_x^2 + f_y^2 = |∇f^2|$

The Attempt at a Solution

Thus I set up the system of equations and solved the quadratic which resulted. However this seemed wrong to me, and I wanted to double check that what I attempted here was correct. Also it seemed like this question should have an easier way to come about a solution. Any guidance would be appreciated

Thank you.

 

[algebrat]

How about if you scale the vector (3,-4) to have length 25?

Hint: what is it's length right now?

(Details: the gradient at a point, points in the direction of steepest change, and it's length is the rate of change of f if we head a unit in that direction. Thus this is the magnitude and direction. It should be easy to find the x and y components of your gradient.)

 

[ozone]

Thanks I got it now. Jeez that was easy like I knew it was. I think I was having a brainfart earlier.