Optimization Area (one vertex on curve) | Mathematics | Page 1

wicked nexus Feb 25, 2023, 4:14 PM

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Need to find length and width given maximized area, been working on this for like four days straight idk how to solve. Any help much appreciated

lean grottoBOT Feb 25, 2023, 4:14 PM

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lunar stump Feb 25, 2023, 7:51 PM

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Consider x=1. What does the rectangle look like?

empty umbra Feb 26, 2023, 5:03 AM

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The length of the rectangle is $e^{-x}^2$ while its base has the breadth x. So your area as a function of a is $e^{-x}^2 x$. Find its maxima and you're done.

cunning quartzBOT Feb 26, 2023, 5:04 AM

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SirLance013
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empty umbra Feb 26, 2023, 5:05 AM

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Your value of $x$ is $\frac{1}{\sqrt(2)}$

cunning quartzBOT Feb 26, 2023, 5:06 AM

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SirLance013

empty umbra Feb 26, 2023, 5:08 AM

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(Here you can see the maxima. Red=your function and blue=${\frac{1}{\sqrt(2)}}$)

#Optimization Area (one vertex on curve)