   Chapter 4.7, Problem 8E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Find the dimensions of a rectangle with area 1000 m2 whose perimeter is as small as possible.

To determine

To find: The dimension of the rectangle with area 1000 m2 whose perimeter is as small as possible.

Explanation

Given:

The area of the rectangle = 1000 m2 .

Calculation:

Let the length and width of the rectangle are x and y respectively.

Therefore the perimeter of the rectangle is p=2(x+y) .

The area is xy=1000 .

y=1000x

Substitute these values in p,

p=2x+2000x

Differentiation with respect to x ,

dpdx=220001x2

For critical points,

dpdx=021x2(x21000)=0x=±1000

Differentiate with respect to x again,

d2pdx2=()

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