What is the extreme f(x)= x/(x^2+1),(-1,2) ?

The extreme f(x)= x/(x^2+1),(-1,2) is Maximum(1, 1/2)

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extreme f(x)= x/(x^2+1),(-1,2)

extreme

Maximum (1, \frac{1}{2})

Solution steps

Find the critical points:

x = 1

Domain of

\frac{x}{x ^{2} + 1}, (- 1, 2) : - 1 < x < 2

Find intervals:

Increasing

: - 1 < x < 1,

Decreasing

: 1 < x < 2

Plug the extreme point

x = 1

into

\frac{x}{x ^{2} + 1} \Rightarrow y = \frac{1}{2}

Maximum (1, \frac{1}{2})

What is the extreme f(x)= x/(x^2+1),(-1,2) ?
The extreme f(x)= x/(x^2+1),(-1,2) is Maximum(1, 1/2)