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 AM #1

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- Mar 8th 2013, 11:25 AM #2

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## Re: 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 PM #3

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- Mar 8th 2013, 01:15 PM #4

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- Mar 8th 2013, 01:29 PM #5

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## Re: 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 PM #6

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