What now Batman??? Optimization Problem Cont.....
Okay, found the algebra easier if I made the square "L-x" and let the circle be "x"
the sum of the two areas would be
Circle + Square = 2Pi(x/2Pi)(squared)+((L-x)/4)(squared)
I think that is right. So the next step should be to take a derivative, SO I will do the left hand side first, add the right hand later (this can get ugly looking quickly here):
Left hand side:
x/2Pi for the left hand side
right hand now:
x/2Pi + -L+x/8
so set top to zero
Stuck again, been at this for hours, I know I need to find both max and min, but the L is causing me great problems. The original problem does not address L or ask for it, could I use a simple value of 1 "one" for it, as the ratio of any cut of the wire would apply to all lengths. I need to walk away for a moment, bang my head against a solid object, multiple times (no I will not take a derivative to find v of that), and hope someone reads this a gives me the push in the right direction
Soon to have a headache