# Max/Min Problems

1. Oct 30, 2008

### Riogho

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

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

3. The attempt at a solution

Ditto.

2. Oct 30, 2008

### gabbagabbahey

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)

3. Oct 30, 2008

### Riogho

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

4. Oct 30, 2008

### gabbagabbahey

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

5. Oct 30, 2008

### Riogho

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

6. Oct 30, 2008

### HallsofIvy

Staff Emeritus
Yes, now do it!

7. Oct 30, 2008

Done.

Many thanks.