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

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

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

extreme points

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

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

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

Maximum (- 1, 2)

Plug

x = 1

into

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

Minimum (1, 0)

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

f (x) = x^{\frac{4}{5}} (x - 4)

\frac{x ^{2} - x}{8 x ^{2} + 1}

(5 - x)^{3}

f (x) = y^{x}

f (x) = - x^{2} + 3 x - 5

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