What is the extreme f(x)= 1/x+2ln(x+3) ?

The extreme f(x)= 1/x+2ln(x+3) is Maximum(-1,-1+2ln(2)),Minimum(3/2 , 2/3+2ln(9/2))

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extreme f(x)= 1/x+2ln(x+3)

extreme points

f (x) = \frac{1}{x} + 2 ln (x + 3)

Maximum (- 1, - 1 + 2 ln (2)), Minimum (\frac{3}{2}, \frac{2}{3} + 2 ln (\frac{9}{2}))

Solution steps

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

Find intervals:

Increasing

: - 3 < x < - 1,

Decreasing

: - 1 < x < 0,

Decreasing

: 0 < x < \frac{3}{2},

Increasing

: \frac{3}{2} < x < \infty

Plug

x = - 1

into

\frac{1}{x} + 2 ln (x + 3) : - 1 + 2 ln (2)

Maximum (- 1, - 1 + 2 ln (2))

Plug

x = \frac{3}{2}

into

\frac{1}{x} + 2 ln (x + 3) : \frac{2}{3} + 2 ln (\frac{9}{2})

Minimum (\frac{3}{2}, \frac{2}{3} + 2 ln (\frac{9}{2}))

Maximum (- 1, - 1 + 2 ln (2)), Minimum (\frac{3}{2}, \frac{2}{3} + 2 ln (\frac{9}{2}))

\frac{1}{x - 6}

p (x) = tan (x) + \frac{1}{x}

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

1.204 e^{8.8448 x}

(3, 0), (0, - 4)

What is the extreme f(x)= 1/x+2ln(x+3) ?
The extreme f(x)= 1/x+2ln(x+3) is Maximum(-1,-1+2ln(2)),Minimum(3/2 , 2/3+2ln(9/2))