# Max/Min Problems

## Homework Statement

A rectangle is bounded by the X-axis and the semicircle Y = [(sqrt)36-x^2]. What dimensions should the rectangle have so that its area is a maximum.

## Homework Equations

Just a note, the 36-x^2 is all under the radical.

## The Attempt at a Solution

Ditto.

gabbagabbahey
Homework Helper
Gold Member
Well, the width of the rectangle is clearly $2x$, and its height is $y=\sqrt{36-x^2}$....so what is its area $A(x)=?$ for a given value of $x$? How do you find the maximum of such a function?

P.S. I don't think the definition of "ditto" is exactly what you seem to think it is (just a friendly FYI)

Wouldn't I just find the area by multiplying both of them together?

gabbagabbahey
Homework Helper
Gold Member
Sounds good to me; the last time I checked the area of a rectangle was just width times height ;0)

So I multiply them together then take the derivative, and then find the critical points of that?

HallsofIvy
Homework Helper
Yes, now do it!

Done.

Many thanks.