1. ## Optimizations... Clueless

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?

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

$A = 3r^2\sin(2\theta)$ , $0 < 2\theta < \frac{\pi}{2}$