I am really stuck on this, the instructor went over the problem in class but I couldn't follow what was happening or why.
A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is vent into a circle. How should the wire be cut so that the total area enclosed is a maximum and B) a minimum.
So here is where I get confused, this is how I set up the problem.
square + circle = 10m
$4s + 2\pi r = 10$ where s is side of a square and r is radius of the circle
and $s^2 + \pi r ^2 = area$
$(\frac{10-2\pi r}{4})^2 + \pi r^2 = 10$
then I take the derivative
$\frac {-10\pi + 2\pi ^2}{4} + 2 \pi$
then I attempt to find zeroes
now I realize that I really messed this up so I have to start all over. I will edit that back in in 20 or so minutes.
I see what I did wrong, the derivative should be
$\frac {-10\pi + 2\pi ^2}{4} + 2 \pi r$
which gives me zeroes of
$ x = \frac {5- \pi}{4}$
so what I did was solve for one variable and plug it into the area formula and then find a min or a max. This was very wrong and I don't know why. For some reason the teacher used 10-x and x for the lengths of wire but I do not see why that is necessary or why my set up is wrong.