# Optimization Problem

• Apr 20th 2009, 05:51 PM
rust1477
Optimization Problem
I am told to maximize the area of a rectangular area within the graph

$y=3e^{-8x^2+2}$

And the area equation I came up with is $A=2xy$

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.
• Apr 20th 2009, 06:04 PM
Calculus26
now use your expression y = 3e^(-8x^2+2)

in A = 2xy and you're good to go
• Apr 20th 2009, 06:19 PM
rust1477
Quote:

Originally Posted by Calculus26
now use your expression y = 3e^(-8x^2+2)

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

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

$2(3e^{-8x^2+2})+3e^{-8x^2+2} * -16x *2x$

I'm pretty sure this is correct so far...
• Apr 20th 2009, 07:41 PM
Calculus26
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