   Chapter 4.7, Problem 14E Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Solutions

Chapter
Section Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

Minimum Perimeter In Exercises 13 and 14, find the length and width of a rectangle that has the given area and a minimum perimeter.Area: A square centimeters

To determine

To calculate: The dimensions of the rectangle that provide the minimum perimeter under the specified conditions where area of the rectangle is A square feet.

Explanation

Given:

The area of the rectangle is A square feet.

Formula Used:

For a function f that is twice differentiable on an open interval I, if f'(c)=0 for some c, then,

If f''(c)>0 the function f has relative minima at c if f''(c)<0 the function f has relative maxima at c. If f''(c)=0, the test fails.

Calculation:

Consider the length and the breadth of the rectangle to be x and y.

Then the quantity to be minimized or the primary equation is:

P=2(x+y)

The perimeter of the rectangle is A square units. This gives:

xy=Ay=Ax

Substitute this back in the primary equation to obtain:

P=2(x+Ax)

Here as both the length and breadth are positive and the area is 49, the feasible domain is:

0xx

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