Question

Calculus Optimization problem (Photo attached momentarily, i'm only having trouble with part C.)

Answer 1

The coordinate P can be described as (x, 1-x), which I understand. The area of the rectangle can then obviously be described as (2x) [the entire base] * (1-x) [the height]. That will give you 2x - 2x^2. Deriving that because if it is presumably graphed, it will have a maximum or minimum where the area will be the most it can possibly be, we will get 2-2x = 0, assuming that the maximum is where the slope of the tangent line equals zero. But then you just get x = 1, and that isn't on the interior of the domain, because x obviously must be less than 1 if it is inscribed! Can anybody help me on this? If anyone needs me to justify my reasoning for any of the previous conclusions, I can do that, just ask, but i'm pretty incredibly sure that they're correct.

Answer 2

u have a little mistake in taking derivative\[(2x-2x^2)'=2-4x\]

Answer 3

Oh, duh, thanks very much.