A piece of wire 12 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle.

A wire of length 12" can be bent into a circle, a square or cut into 2 pieces and make both a circle and a square. How much wire should be used for the circle if the total area enclosed by the figure (s) is to be:

a) a Maximum

b) a Minimum

What I've got so far is that the formula for the square is As=116s2

and the circumfrance of the circle to be P=12-c

and area to be Ac=π (P2π) 2

where c

is the length of the wire for the circle and s

is the length of the wire for the square.

Now I know I need to differentiate these formulas to then find the max and min they both can be, but what am I differentiating with respect to? The missing variable in each of the formulas?

Also, once, I find the derivitives, what would my next steps be to minimizing and maximizing these?

And did I set the problem up correctly?