Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Gradient Vector- largest possible rate of change?

  1. Mar 8, 2016 #1

    My professor just gave us a True or False problem that states:

    ∇H(x,y), the gradient vector of H(x,y), gives us the largest possible rate of change of H at (x,y).

    Now, he said the answer is true, but it was my understanding that the gradient itself gives the direction of where the function increases fastest. And then in order to find the maximum rate of change, you have to find the magnitude of the gradient vector and plug in the point to the function.

    Is there some flaw in my understanding?

  2. jcsd
  3. Mar 8, 2016 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    The gradient contains information on both the direction and maximal rate of change. The magnitude is a property of a vector.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Gradient Vector- largest possible rate of change?
  1. The gradient vector (Replies: 8)

  2. Gradient Vector (Replies: 7)

  3. Gradient of a vector (Replies: 4)