   Chapter 4.3, Problem 92E ### 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

# For what values of c is the function f ( x ) = c x + 1 x 2 + 3 increasing on (−∞, ∞)?

To determine

To find: The value of c when the function f(x)=cx+1x2+3 is increasing on (,) .

Explanation

The given function is, f(x)=cx+1x2+3 .

Obtain the derivative of f(x) .

f(x)=ddx(cx+1x2+3)=c(1)+(1(x2+3)2(2x))=c2x(x2+3)2

Since f(x) is increasing on (,) then, the first order derivative f(x)>0 on the interval (,)

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 