Optimization functions?

Question

I do not know how to figure out this problem. Please help.

What is the area of the largest rectangle that can be inscribed in the region bounded by y=3-x^2 and the x-axis?

Thanks!

Answer 1

A = y*x

A = (3 - x^2) (x) = 3x - x^3

A' = 3 - 3x^2 = 0

x = ±1

y = 3 - 1^2 = 2

Therefore, Area is maximized at x = ±1 and y = 2

A = 2*2(1) = 4 units^2

Answer 2

just follow the limits ex: as x approaches the sqr3 it get smaller

after    bigger

hence, it looses continuity in regard to itself.

So the largest rec. would be x= +or - sqr3 while y=1 (its value is not needed) using +y and -y.  Use these four corners.

Answer 3

basically just graph that equation and then put a rectangle in the boundaries created by that and the xaxis and see how big it goes