# Optimizations... Clueless

• November 9th 2010, 12:55 PM
ursapine
Optimizations... Clueless
Attachment 19650
Consider a symmetric cross inscribed in a circle of radius r:

A. Write the area A of the cross as a function of x and find the value of x that maximizes the area.
B. Write the area A of the cross as a function of θ and find the value of θ that maximizes the area.
C. Show that the critical numbers of parts (a) and (b) yield the same maximum area. What is that area?

• November 9th 2010, 02:31 PM
skeeter
Quote:

Originally Posted by ursapine
Consider a symmetric cross inscribed in a circle of radius r:

A. Write the area A of the cross as a function of x and find the value of x that maximizes the area.
B. Write the area A of the cross as a function of θ and find the value of θ that maximizes the area.
C. Show that the critical numbers of parts (a) and (b) yield the same maximum area. What is that area?
http://www.mathhelpforum.com/math-he...s-untitled.jpg

$A = 6x\sqrt{r^2-x^2}$ , $0 < x < r$

$A = 3r^2\sin(2\theta)$ , $0 < 2\theta < \frac{\pi}{2}$
• November 9th 2010, 05:04 PM
ursapine