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

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

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

extreme points

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

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

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Decreasing

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

Increasing

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

Plug

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

into

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

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

Plug

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

into

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

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

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

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

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

x x^{2} + 25

f (x, y) = 2 x^{2} + 3 x y + 4 y^{2} + 2 x - 10 y

f (x) = x e^{- 6 x}, 0 \leq x \leq 2

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