Problem

The three cases in the First Derivative Test cove…

12:19

Problem 92 Medium Difficulty

For what values of $ c $ is the function
$$ f(X0 = cx + \frac{1}{x^2 + 3} $$
increasing on $ (-\infty, \infty) $?

Answer

For all $c>\frac{1}{8} \quad f(x)$ is increasing on $(-\infty,+\infty)$

Topics

Derivatives

Differentiation

Volume

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 3

How Derivatives Affect the Shape of a Graph

Discussion

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Watch More Solved Questions in Chapter 4

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Video Transcript

Okay, So rest. For what? About gypsies that function after effects. Because here, because one of the exquisite street is increasing from negative infinity infinity. So first, we're gonna take the first derivative. So when you think the derivative we get so you might have to act over X square plus three squared and we have to set this equal to greater than zero, and then you can bring the sea over. So when you do that you get to see is greater than two acts over expert Plus three, and that's squared. And so where does this occur? Or yes, Leo, it's just if you grafted. And so you're looking for where there is some sort of wars on attention, she and when you go out the function, the words on attention that's that one comma zero point one two five. So that means the value of sea has to be greater than your point one two five for this to be true, and that's it.

Fahad P.

Topics

Derivatives

Differentiation

Volume

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 3

How Derivatives Affect the Shape of a Graph

Top Calculus 2 / BC Educators

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University

Kristen K.

University of Michigan - Ann Arbor

Joseph L.

Boston College