there is one critical point for z=yx^5 + xy^5 + xy. Find it.

Is the critical point (0,0)?

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- Mar 8th 2013, 11:07 AMapatitemax/min
there is one critical point for z=yx^5 + xy^5 + xy. Find it.

Is the critical point (0,0)? - Mar 8th 2013, 11:25 AMShakarriRe: max/min
There is a critical point when dz/dy and when dz/dx are equal to zero

dz/dx= 5yx^{5y-1}+ y^{5}+ y

This is zero at (0,0)

dz/dx= x^{5y}lnx^{5}+ 5xy^{4}+ x

This is not defined at (0,0) because ln0 is not defined.

I do not know how to find the critical point but (0,0) is not it - Mar 8th 2013, 01:10 PMapatiteRe: max/min
.....

- Mar 8th 2013, 01:15 PMapatiteRe: max/min
- Mar 8th 2013, 01:29 PMHallsofIvyRe: max/min
Okay, so what

**are**$\displaystyle \partial z/\partial x$ and $\displaystyle \partial z/\partial y$? Where are they both equal to 0?

By the way, in response to Shakarri's comment, a critical point is where the derivative is 0**or**where the derivative does not exist. - Mar 8th 2013, 01:57 PMapatiteRe: max/min