   Chapter 4.7, Problem 4E ### 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

# The sum of two positive numbers is 16. What is the smallest possible value of the sum of their squares?

To determine

To find:  The smallest possible value of the sum of squares of two numbers whose sum is 16.

Explanation

Given:

The sum of two numbers = 16

Formula used: (ab)2=a22ab+b2

Calculation:

Consider two numbers be x and y .

The sum of two numbers x+y=16 .

The sum of the square is S = x2+y2 .

Rewrite the equation x+y=16 as follows

y=16x

Substitute the value of y in S,

S=x2+(16x)2=x2+25632x+x2=2x232x+256

Differentiate with respect to x ,

dSdx=4x32

For critical points,

dsdx=0

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