1. ## max/min

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

Is the critical point (0,0)?

2. ## Re: max/min

There is a critical point when dz/dy and when dz/dx are equal to zero
dz/dx= 5yx5y-1+ y5+ y
This is zero at (0,0)

dz/dx= x5ylnx5+ 5xy4+ 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

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4. ## Re: max/min

Originally Posted by Shakarri
There is a critical point when dz/dy and when dz/dx are equal to zero
dz/dx= 5yx5y-1+ y5+ y
This is zero at (0,0)

dz/dx= x5ylnx5+ 5xy4+ 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
Sorry, its yx^5 not x^5y

5. ## Re: max/min

Okay, so what are $\partial z/\partial x$ and $\partial z/\partial y$? 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.

6. ## Re: max/min

Originally Posted by HallsofIvy
Okay, so what are $\partial z/\partial x$ and $\partial z/\partial y$? 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.
fx(x,y)= 5yx^4+y^%+y
fy(x,y)= x^5+5xy^4+x

so x=0 and y=0?