# I need help!

• March 27th 2008, 10:33 AM
113918
I need help!
• March 27th 2008, 11:05 AM
TheEmptySet
Here is #2
we know that

$x-y=24 \mbox{ and } A=xy$

We want to minimize A

subbing the first into the second we get...

$A=(y+24)y=y^2+24y$

Since we want the minimum value we need to find the vertex of the parabola.

There are a few different ways. Since it is symmetric about its vertex the vertex is half way between its intercepts -24 and 0 so at -12

or we could use the vertex fromula

$y=\frac{-b}{2a}=\frac{-24}{2(1)}=-12$

Now that we know y we can solve for x

$x-(-12)=24 \iff x=12$

so the minimum product is $x \cdot y =(12)(-12)=-144$