What is the extreme 5x+1+2/(x-2) ?

The extreme 5x+1+2/(x-2) is Maximum(-sqrt(2/5)+2,11-2sqrt(10)),Minimum(sqrt(2/5)+2,2sqrt(10)+11)

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extreme 5x+1+2/(x-2)

extreme points

5 x + 1 + \frac{2}{x - 2}

Maximum (- \frac{2}{5} + 2, 11 - 210), Minimum (\frac{2}{5} + 2, 210 + 11)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < \frac{2 5 - 2}{5},

Decreasing

: \frac{2 5 - 2}{5} < x < 2,

Decreasing

: 2 < x < \frac{2 5 + 2}{5},

Increasing

: \frac{2 5 + 2}{5} < x < \infty

Plug

x = - \frac{2}{5} + 2

into

5 x + 1 + \frac{2}{x - 2} : 11 - 210

Maximum (- \frac{2}{5} + 2, 11 - 210)

Plug

x = \frac{2}{5} + 2

into

5 x + 1 + \frac{2}{x - 2} : 210 + 11

Minimum (\frac{2}{5} + 2, 210 + 11)

Maximum (- \frac{2}{5} + 2, 11 - 210), Minimum (\frac{2}{5} + 2, 210 + 11)

f (x) = x^{3} - 3 x + 8

y = (x^{2} - 3) e^{x}

f (x) = x^{3} - 3 x - 5

f (x) = 3 x^{2} + 6 x + 1

f (x) = 4 - 3 x

What is the extreme 5x+1+2/(x-2) ?
The extreme 5x+1+2/(x-2) is Maximum(-sqrt(2/5)+2,11-2sqrt(10)),Minimum(sqrt(2/5)+2,2sqrt(10)+11)