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

The extreme y=(x^2+1)/(x+1) is Maximum(-1-sqrt(2),-2sqrt(2)-2),Minimum(-1+sqrt(2),2sqrt(2)-2)

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

extreme points

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

Maximum (- 1 - 2, - 22 - 2), Minimum (- 1 + 2, 22 - 2)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1 - 2,

Decreasing

: - 1 - 2 < x < - 1,

Decreasing

: - 1 < x < - 1 + 2,

Increasing

: - 1 + 2 < x < \infty

Plug

x = - 1 - 2

into

\frac{x ^{2} + 1}{x + 1} : - 22 - 2

Maximum (- 1 - 2, - 22 - 2)

Plug

x = - 1 + 2

into

\frac{x ^{2} + 1}{x + 1} : 22 - 2

Minimum (- 1 + 2, 22 - 2)

Maximum (- 1 - 2, - 22 - 2), Minimum (- 1 + 2, 22 - 2)

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

y = 2 x - x^{2}

110 \cdot 3. 1^{x}

\frac{8}{3} x - 3

f (x) = x + 2 sin (x)

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