What is the extreme ((x+1)^2)/(1+x^2) ?

The extreme ((x+1)^2)/(1+x^2) is Minimum(-1,0),Maximum(1,2)

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extreme ((x+1)^2)/(1+x^2)

extreme

Minimum (- 1, 0), Maximum (1, 2)

Solution steps

f^{'} (x) = \frac{- 2 x ^{2} + 2}{( 1 + x ^{2} ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

\frac{( x + 1 ) ^{2}}{1 + x ^{2}} : 0

Minimum (- 1, 0)

Plug

x = 1

into

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

Maximum (1, 2)

Minimum (- 1, 0), Maximum (1, 2)

What is the extreme ((x+1)^2)/(1+x^2) ?
The extreme ((x+1)^2)/(1+x^2) is Minimum(-1,0),Maximum(1,2)