• Support PF! Buy your school textbooks, materials and every day products Here!

Specific slope for directional derivative?

  • Thread starter glog
  • Start date
  • #1
17
0
Is there a direction where the rate of change is 18, at the point (-1,2) on the function f(x,y) = (x^2)(y^3)+xy?

So I found the gradient of this function, picked a random direction vector u = ( a / (a^2+b^2)^(1/2) , b / (a^2+b^2)^(1/2) ) and took the dot product, and set it to 18... however, I have one equation with two unknowns and no idea how to proceed.

Thank you.
 

Answers and Replies

  • #2
378
2
Is there a direction where the rate of change is 18, at the point (-1,2) on the function f(x,y) = (x^2)(y^3)+xy?

So I found the gradient of this function, picked a random direction vector u = ( a / (a^2+b^2)^(1/2) , b / (a^2+b^2)^(1/2) ) and took the dot product, and set it to 18... however, I have one equation with two unknowns and no idea how to proceed.

Thank you.
don't do that mess..

just say u = <a,b> is unit vector
so, a^2+b^2 = 1 would be your second equation
and
<a,b>.del f = 18 your first equation

I found del f to be <-14,11>
this might be wrong, because I didn't recheck my work
 
  • #3
Defennder
Homework Helper
2,591
5
It doesn't matter if you have 2 unknowns. You're interested in the direction, not the magnitude of the direction vector. Express either a or b in terms of the other and then normalise the vector (a,b)
 

Related Threads for: Specific slope for directional derivative?

  • Last Post
Replies
1
Views
648
  • Last Post
Replies
4
Views
1K
Replies
10
Views
3K
  • Last Post
Replies
2
Views
5K
Replies
8
Views
1K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
21
Views
3K
Top