Question

Find the largest possible area for a rectangle with base on the x-axis and upper vertices on the curve

Answer 1

So here is how we find the answer to this given problem.
The formula for area is: A=(l)(w)
So, A=(2x)(8-x²)
A=16x-2x³
dA/dx = 16-6x²
then you will use calculus to get the absolute local maximum of x by letting dA/dx = 0
then wha you will get is x = 2sqrt(6)/3
so the area would be= 64 * sqrt(6) / 9
or 64√6/9.
Based on the choices given, the answer would be option D. 
Hope this answer helps.