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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Find two positive numbers whose product is 100 and whose sum is a minimum.

To determine

To find: The two positive numbers whose product is 100 such that their sum is minimum.

Explanation

Calculation:

Let two numbers be x and y.

The product of these two numbers is 100. That is, xy=100 .

So, y=100x .

Let S be the sum of these two numbers. That is, S=x+y .

Substitute y=100x in S,

S=100x+x

Differentiate the above expression with respect to x,

dSdx=100x2+1

For critical numbers, dSdx=0

100x2+1=0x2=100x=±10

As only positive values are accepted, x=10

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