Optimization Problem

I am told to maximize the area of a rectangular area within the graph



And the area equation I came up with is

I understand optimization problems just fine and I know the above equations are correct, I'm just having a lot of trouble simplifying my answer. If anyone cares to take a look at it, that'd be swell.

now use your expression y = 3e^(-8x^2+2)

in A = 2xy and you're good to go

Quote:

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Originally Posted by Calculus26

now use your expression y = 3e^(-8x^2+2)

in A = 2xy and you're good to go

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Yes I can get that far, putting that into A=2xy and taking the derivative yields



I'm pretty sure this is correct so far...

OK now when you set the derivative equal to 0 cancel out the exponential because it is always positive

6- 96x^2 = 0

x^2 = 1/16

x = 1/4