Thread: Extrema

Hello,

yesterday we had a test of calculus and one question was:

Find and classify the extreme of
h(x,y)=(1+1/(x))*(1+1/(y))*(1/(x)+1/(y))

I have absolutely no idea how to solve this thing. Can someone help me?

Greets,
Leslon

Originally Posted by Leslon

Hello,

yesterday we had a test of calculus and one question was:

Find and classify the extreme of
h(x,y)=(1+1/(x))*(1+1/(y))*(1/(x)+1/(y))

I have absolutely no idea how to solve this thing. Can someone help me?

Greets,
Leslon

An extrema is a local minimum or maximum within a function. This is when

You have

Let's first try to simplify this...







Can you derive this?

Well if I derive this, I get:
-(1+1/y)*(1/x+1/y)/x^2-(1+1/x)*(1+1/y)/x^2 for dh(x,y)/dx

and

-(1+1/x)*(1/x+1/y)/y^2-(1+1/x)*(1+1/y)/y^2 for dh(x,y)/dy

and now I'm stuck..

What to do next??

PS: I've included a .tex file if necessary

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I know it works that way on some sites, but the way it works here is better.