
I need help!

Here is #2
we know that
$\displaystyle xy=24 \mbox{ and } A=xy$
We want to minimize A
subbing the first into the second we get...
$\displaystyle A=(y+24)y=y^2+24y$
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
$\displaystyle y=\frac{b}{2a}=\frac{24}{2(1)}=12$
Now that we know y we can solve for x
$\displaystyle x(12)=24 \iff x=12$
so the minimum product is $\displaystyle x \cdot y =(12)(12)=144$