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Could anyone tell me where is my mistake? I took the derivative and I solved for r and ended up with this answer

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Can you show the formula you found for the derivative? The problem takes more than one step to solve, impossible to guess where you went wrong without seeing some intermediate steps. –  David K Jul 3 at 3:01
    
What is $A$? ${}{}{}$ –  copper.hat Jul 3 at 3:03
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$P'(r)=(2+\pi/2-A/r^2)$ So $P'(r)=0$ implies that $r=\sqrt{\frac{A}{2+\frac{\pi}{2}}}$. You can also see that $P''$ at this point is positive and hence gives a absolute minimum for your perimeter function. It is best not to simplify terms such as $2+\pi/2$ into a decimal. Your online homework program wants exact answers and not approximations. To justify that the $r$ we found above indeed gives an absolute minimum, you can also use the first derivative test for absolute extrema. (if that's what you've been taught)

Just to clarify: $2+\frac{\pi}{2}$ is exact but the approximation $3.5708$ is not exact but an approximation to the correct answer. You should keep this in mind when you use these online homework programs. It rejected your answer because it wanted the answer in the exact form.

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Yeah I thought it might because of the pi –  user157908 Jul 3 at 3:18
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