• anonymous
find all the critical points of the following function. indicate whether each point is a local max, min or a saddle point.\[f(x,y)=x ^{3}-y ^{3}-2xy+6\]
  • Stacey Warren - Expert
Hey! We 've verified this expert answer for you, click below to unlock the details :)
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.
  • jamiebookeater
I got my questions answered at in under 10 minutes. Go to now for free help!
  • .Sam.
\[\max =\frac{170}{27}\text{ at }(x,y)=\left(-\frac{2}{3},\frac{2}{3}\right)\]
  • anonymous
would you mind to show your working on obtaining \[(\frac{-2}{3}, \frac{2}{3})\]? because when i tried to find the value of y when x is -2/3, i got +-2/3 for y; and when i use (-2/3, 2/3) to determine max or mine, the discriminant D equals to 0.
  • anonymous
\[D=f _{xx}f _{yy}-f _{xy }^{2}\]

Looking for something else?

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