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(a) Show that of all the rectangles with a given area, the one with smallest perimeter is a square.(b) Show that of all the rectangles with a given area, the one with greatest area is a square.

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04:40

Wen Zheng

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 7

Optimization Problems

Derivatives

Differentiation

Volume

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Lectures

04:35

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

06:14

A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

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(a) Show that of all the r…

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$\begin{array}{l}{\text { …

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Show that of all the recta…

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we know that if l w is A than P is to l plus two w meaning that two outposts to a over l is gonna be p which gives us p prime. In other words, the derivative is gonna be to minus too, huh? Overall squared. So that's equal to zero When we get our equals square root of a this means w a squirt of it w and our both equivalent discord of Ed, which indicates that because the with equals the length, the rectangle, the smallest perimeter is indeed the shape of a square. Now moving on to part B, we know we can rearrange. You are link terms with equals A to write it in terms of the west length plus with equals perimeter over to their fur with his perimeter over to minus length. They're for the area is length times permit over to minus length squared. Therefore, a prime is p over to Ryan's to Elsa this equal to zero. So for out on me, get out. Is Pete over four Now do the same thing for w we get w is also pee over, for they are equivalent. Therefore, l is equivalent to W. Therefore, we know that because length equals with of our tingle with the maximum area is a square

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