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# 2 Maximizing rectangle perimeters All rectangles with an ISBN: 9780321570567 2

## Solution for problem 46E Chapter 4.1

Calculus: Early Transcendentals | 1st Edition

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Problem 46E

2 Maximizing rectangle perimeters All rectangles with an area of 64 m have a perimeter given ? by P(? ) = 2 x + 128/x. ?wher? is the length of one. side of the rectangle. Find the absolute minimum value of the perimeter function. What are the Dimensions of the rectangle with minimum perimeter?

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STEP_BY_STEP SOLUTION Step-1 Let f be a continuous function defined on an open interval containing a 1 number ‘c’.The number ‘c’ is critical value ( or critical number ). If f (c) 1 = 0 or f (c) is undefined. A critical point on that graph of f has the form (c,f(c)). Step-2 When an output value of a function is a maximum or a minimum over the entire domain of the function, the value is called the absolute maximum or the absolute minimum. Let f be a func tion with domain D and let c be a fixed constant in D . Then the output value f( ) is the 1. Absolute maximum value of f on D if and only if f(x) f(c) , for all x in D. 2. Absolute minimum value of f on D if and only if f(c) f(x) , for all x in D. Step_3 Given that ; x is the length of one side of the rectangle. Area of the rectangle is 64 m 2 128 Perimeter of the given rectangle is P(x) = 2x+ x .Clearly P(x) is a rational function and it is continuous for all x ,except zero. But here x is length of a rectangle , so it takes only positive values .Hence the function...

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##### ISBN: 9780321570567

Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The full step-by-step solution to problem: 46E from chapter: 4.1 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This full solution covers the following key subjects: perimeter, rectangle, minimum, maximizing, function. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. Since the solution to 46E from 4.1 chapter was answered, more than 309 students have viewed the full step-by-step answer. The answer to “2 Maximizing rectangle perimeters All rectangles with an area of 64 m have a perimeter given ? by P(? ) = 2 x + 128/x. ?wher? is the length of one. side of the rectangle. Find the absolute minimum value of the perimeter function. What are the Dimensions of the rectangle with minimum perimeter?” is broken down into a number of easy to follow steps, and 54 words.

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