A piece of wire of length 60 is cut, and the resulting two pieces are formed to make a circle and a square. Where should the wire be cut to (a) minimize and (b) maximize the combined area of the circle and square?
So Area of circle and square= pir^2 +x^2 perimeter of circle and square = 2pir+4x
Solve for r: 2pir+4x=60 r=30-2x/pi
plug r into area equation
pi(30-2x/pi)^2+x^2=area (30-2x)^2/pi + x^2=
find derivative to get CP for min/max
A(X)=(30-2x)^2/pi + x^2 A'(x)= (-120+2x/pi)+2x
therefore, x=60 and x=0.
Now at this point I know that if I plug in 60 and 0 in the original area function, it will give me a number then I can compare those numbers and see where is it largest at what x value. But how would I find the minimum value exactly?