Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

richyw

  • 2 years ago

question about critical points...

  • This Question is Closed
  1. richyw
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Hi, I have been unable to find this in my textbook. So say I have \(f(x,y)\) at the point \((a,b)\) and \[\frac{\partial f}{\partial x}=\frac{\partial f}{\partial y}=0\]

  2. richyw
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    If I say \[\Delta(x,y)=\frac{\partial^2 f}{\partial x^2}\cdot\frac{\partial^2 f}{\partial y^2}-\left(\frac{\partial^2f}{\partial x\partial y}\right)^2\]

  3. richyw
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    then if \[\Delta (a,b) > 0\quad \text{and}\quad \frac{\partial^2f}{\partial x\partial y}>0\] I have a relative maximum. And if\[\Delta (a,b) > 0\quad \text{and}\quad \frac{\partial^2f}{\partial x\partial y}<0\]I have a relative minimum.

  4. richyw
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    If \(\Delta (a,b) < 0\) I have a saddle point. And If \(\Delta (a,b) = 0\) I can't draw any conclusions. So I have two questions. The first one (most important) is what if \[\frac{\partial^2f}{\partial x\partial y}=0\] Then how do I know if this is a maximum or a minimum? The second question (less important for now), is why does this work!?!?

  5. richyw
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sorry the mixed partial derivatives are also evaluated at (a,b)

  6. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.