`f(x) = (4x)/(x^2 + 1)` Find the critical numbers of the function.

Textbook Question

Chapter 3, 3.1 - Problem 14 - Calculus of a Single Variable (10th Edition, Ron Larson).
See all solutions for this textbook.

1 Answer | Add Yours

mathace's profile pic

mathace | (Level 3) Assistant Educator

Posted on

GivenĀ `f(x)=(4x)/(x^2+1)`

Find the derivative using the Quotient Rule. The set the derivative equal to zero and solve for the critical x value(s).

`f'(x)=[(x^2+1)(4)-(4x)(2x)]/(x^2+1)=0`

`f'(x)=4x^2+4-8x^2=0`

`f'(x)=-4x^2+4=0`

`f('x)=-4(x^2-1)=0`

`x=1,x=-1`

We’ve answered 318,944 questions. We can answer yours, too.

Ask a question