Maximize P = xy with x + y = 6.

Question

ryan123345 · Answer

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anonymous · Answer

P = x(6-x)
   = -x^2 + 6x

Now use first derivative test to differentiate P w.r.t x and find the critical points

anonymous · Answer

Without calculus, you can find the vertex of the parabola by using x=-b/2a with a=coefficient of square term and b=coefficient of x to first power term.  Once you find x, substitute it back into your equation to find y, and this will be your maximum value.