Question

Determine the value of x so that the rectangle has max. area, where A=xy, y= 8-x^2, 0 12 years ago

Answer 1

A=x(8-x^2)

explicit way is to solving \( \large \frac{d}{dx} A=0 \) and then find maximum of A

Answer 2

is possible for you to solve for max of A, if not i understand. i appreciate the help

Answer 3

actually u need to find the abs. max of A on the interval (0,2sqrt2]
first step is Finding critical points. Compute A'(x)

Answer 4

okay thanks

Answer 5

A(x)=8x-x^3 and A'(x)=8-3x^2 A'(x)=0 -----> 8=3x^2 ---> \(\large x=\pm \frac{\sqrt{3}}{2\sqrt{2}} \) we choose positive sign because negative sign is not on our interval

Answer 6

now we must check \( \sqrt{2} \) and \(\large \frac{\sqrt{3}}{2\sqrt{2}} \)