What is the extreme f(x)=5x+1+1/(x-1) ?

The extreme f(x)=5x+1+1/(x-1) is Maximum(-sqrt(1/5)+1,6-2sqrt(5)),Minimum(sqrt(1/5)+1,2sqrt(5)+6)

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extreme f(x)=5x+1+1/(x-1)

extreme points

f (x) = 5 x + 1 + \frac{1}{x - 1}

Maximum (- \frac{1}{5} + 1, 6 - 25), Minimum (\frac{1}{5} + 1, 25 + 6)

Solution steps

f^{'} (x) = - \frac{1}{( x - 1 ) ^{2}} + 5

Find intervals:

Increasing

: - \infty < x < \frac{5 - 1}{5},

Decreasing

: \frac{5 - 1}{5} < x < 1,

Decreasing

: 1 < x < \frac{1 + 5}{5},

Increasing

: \frac{1 + 5}{5} < x < \infty

Plug

x = - \frac{1}{5} + 1

into

5 x + 1 + \frac{1}{x - 1} : 6 - 25

Maximum (- \frac{1}{5} + 1, 6 - 25)

Plug

x = \frac{1}{5} + 1

into

5 x + 1 + \frac{1}{x - 1} : 25 + 6

Minimum (\frac{1}{5} + 1, 25 + 6)

Maximum (- \frac{1}{5} + 1, 6 - 25), Minimum (\frac{1}{5} + 1, 25 + 6)

f (x) = x y^{2} - 4 x^{2} - 3 y^{2} + 12 x

4 x^{4} + 4 y^{4} - x y

f (x, y) = ln (x^{3} y + 3 x y^{3})

f (x) = 2 x ln (9 x)

f (x, y) = - x^{4} + y^{4} + x^{2} - y^{2}

What is the extreme f(x)=5x+1+1/(x-1) ?
The extreme f(x)=5x+1+1/(x-1) is Maximum(-sqrt(1/5)+1,6-2sqrt(5)),Minimum(sqrt(1/5)+1,2sqrt(5)+6)