Calculus - Optimization - Rectangle Inscribed in a Semicircle

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We show that the rectangle with maximum area inscribed in a semicircle consists of a square in each of the first and second quadrants.

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Комментарии
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Thank you for helping me learn, your voice makes me want to fall asleep, but you are a helpful man

recouno
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Great video! By the way, if you had to find the largest perimeter instead, would you do the exact same thing except that instead of having A = 2xy, you would have p = 4x + 2y?

ianstange
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Thank you so much, my calc Prof. didn't teach us this in class but it was on the homework.

fitzdettmer
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how can you use the equation for a full circle with a semi circle?

yellowcircle
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Thanks! This question made no sense until I watched this

AntiContent
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This is incorrect. You've forgotten that you're trying to maximize the area of the rectangle, not the circle. So instead of the last step being y=sqrt[a^2-(a/sqrt2)^2] it should be y=2x, and you get y=2a/sqrt2.

This is straight out of calculus text book by Larson and Edwards 10th edition.

raymondspence