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?