What is the extreme f(x)=x+((4))/((x+1)) ?

The extreme f(x)=x+((4))/((x+1)) is Maximum(-3,-5),Minimum(1,3)

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extreme f(x)=x+((4))/((x+1))

extreme points

f (x) = x + \frac{( 4 )}{( x + 1 )}

Maximum (- 3, - 5), Minimum (1, 3)

Solution steps

f^{'} (x) = 1 - \frac{4}{( x + 1 ) ^{2}}

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < - 1,

Decreasing

: - 1 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 3

into

x + \frac{4}{x + 1} : - 5

Maximum (- 3, - 5)

Plug

x = 1

into

x + \frac{4}{x + 1} : 3

Minimum (1, 3)

Maximum (- 3, - 5), Minimum (1, 3)

What is the extreme f(x)=x+((4))/((x+1)) ?
The extreme f(x)=x+((4))/((x+1)) is Maximum(-3,-5),Minimum(1,3)