Question

Optimization:
A rectangle is bounded by the x-axis and the semicircle y= (25-x^2)^1/2 . what length and width should the rectangle have so its area is a maximum?

Answer 1

\[y=\sqrt{25-x^2}\] heres a better view of the equation

Answer 2

see it from here

Answer 3

If you draw such a rectangle such that the base is from -x to x and the height is y, the area is
A = 2xy

Now substitute for y and you have a function A = f(x). Use calculus now to find the maximum of f(x)