Question

Can anyone please help with this question : What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y=12-x^2?

Answer 1

The area of the rectangle is 2a * f(a)

2a * ( 12 - x^2 )
24a - 2a^3

We have to maximize that function

Answer 2

If we look at the plot we can see a maximum of 32 at a=2

You can of course use the derivate of the area-function and look at the zeros of that derivate. It won't change the answer.