What is the extreme f(x)=(1/x)+2+(4/(1-x)) ?

The extreme f(x)=(1/x)+2+(4/(1-x)) is Maximum(-1,3),Minimum(1/3 ,11)

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extreme f(x)=(1/x)+2+(4/(1-x))

extreme

Maximum (- 1, 3), Minimum (\frac{1}{3}, 11)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Decreasing

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

Increasing

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

Increasing

: 1 < x < \infty

Plug

x = - 1

into

\frac{1}{x} + 2 + \frac{4}{1 - x} : 3

Maximum (- 1, 3)

Plug

x = \frac{1}{3}

into

\frac{1}{x} + 2 + \frac{4}{1 - x} : 11

Minimum (\frac{1}{3}, 11)

Maximum (- 1, 3), Minimum (\frac{1}{3}, 11)

What is the extreme f(x)=(1/x)+2+(4/(1-x)) ?
The extreme f(x)=(1/x)+2+(4/(1-x)) is Maximum(-1,3),Minimum(1/3 ,11)