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 $\displaystyle f'(x)=0$
You have $\displaystyle h(x,y) = \left(1+\frac{1}{x}\right)\left(1+\frac{1}{y}\righ t)\left(\frac{1}{y}+\frac{1}{x}\right)$
Let's first try to simplify this...
$\displaystyle h(x,y)=\left(1 + \frac{1}{y} + \frac{1}{x} + \frac{1}{xy}\right) \left(\frac{1}{y}+\frac{1}{x}\right)$
$\displaystyle h(x,y)=\frac{1}{y} + \frac{1}{y^2} + \frac{1}{xy} + \frac{1}{xy^2} + \frac{1}{x}+\frac{1}{xy}+\frac{1}{x^2}+\frac{1}{x^ 2y}$
$\displaystyle h(x,y)=\frac{1}{y} + \frac{1}{y^2} + \frac{2}{xy} + \frac{1}{xy^2} + \frac{1}{x}+\frac{1}{x^2}+\frac{1}{x^2y}$
Can you derive this?