What is the extreme f(x)=3x+1+1/(x-1) ?

The extreme f(x)=3x+1+1/(x-1) is Maximum(-sqrt(1/3)+1,4-2sqrt(3)),Minimum(sqrt(1/3)+1,2sqrt(3)+4)

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extreme f(x)=3x+1+1/(x-1)

extreme points

f (x) = 3 x + 1 + \frac{1}{x - 1}

Maximum (- \frac{1}{3} + 1, 4 - 23), Minimum (\frac{1}{3} + 1, 23 + 4)

Solution steps

f^{'} (x) = - \frac{1}{( x - 1 ) ^{2}} + 3

Find intervals:

Increasing

: - \infty < x < \frac{3 - 1}{3},

Decreasing

: \frac{3 - 1}{3} < x < 1,

Decreasing

: 1 < x < \frac{1 + 3}{3},

Increasing

: \frac{1 + 3}{3} < x < \infty

Plug

x = - \frac{1}{3} + 1

into

3 x + 1 + \frac{1}{x - 1} : 4 - 23

Maximum (- \frac{1}{3} + 1, 4 - 23)

Plug

x = \frac{1}{3} + 1

into

3 x + 1 + \frac{1}{x - 1} : 23 + 4

Minimum (\frac{1}{3} + 1, 23 + 4)

Maximum (- \frac{1}{3} + 1, 4 - 23), Minimum (\frac{1}{3} + 1, 23 + 4)

What is the extreme f(x)=3x+1+1/(x-1) ?
The extreme f(x)=3x+1+1/(x-1) is Maximum(-sqrt(1/3)+1,4-2sqrt(3)),Minimum(sqrt(1/3)+1,2sqrt(3)+4)