richyw
  • richyw
question about critical points...
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
richyw
  • richyw
Hi, I have been unable to find this in my textbook. So say I have \(f(x,y)\) at the point \((a,b)\) and \[\frac{\partial f}{\partial x}=\frac{\partial f}{\partial y}=0\]
richyw
  • richyw
If I say \[\Delta(x,y)=\frac{\partial^2 f}{\partial x^2}\cdot\frac{\partial^2 f}{\partial y^2}-\left(\frac{\partial^2f}{\partial x\partial y}\right)^2\]
richyw
  • richyw
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.

Looking for something else?

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

More answers

richyw
  • richyw
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!?!?
richyw
  • richyw
sorry the mixed partial derivatives are also evaluated at (a,b)

Looking for something else?

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