What is the length of the largest interval on which the function $f ( x ) = \frac { x } { x ^ { 2 } + 1 }$ is increasing?
A)3
B) $2 \sqrt { 3 }$
C) $2 \sqrt { 2 }$
D)1
E)4
F) $\sqrt { 3 }$
G)2

H) $3 \sqrt { 2 }$

Question

What is the length of the largest interval on which the function $f ( x ) = \frac { x } { x ^ { 2 } + 1 }$ is increasing?
A)3
B) $2 \sqrt { 3 }$ 
C) $2 \sqrt { 2 }$ 
D)1
E)4
F) $\sqrt { 3 }$
G)2

H) $3 \sqrt { 2 }$

Quizplus · Accepted Answer

The function $f(x) = \frac{x}{x^2 + 1}$ is increasing where its derivative $f'(x) = \frac{1 - x^2}{(x^2 + 1)^2}$ is positive. Solving $1 - x^2 > 0$ gives the interval $-1 < x < 1$, which has a length of 2.

What Is the Length of the Largest Interval on Which f(x)=xx2+1f ( x ) = \frac { x } { x ^ { 2 } + 1 }f(x)=x2+1x​

What Is the Length of the Largest Interval on Which $f ( x ) = \frac { x } { x ^ { 2 } + 1 }$