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

The extreme f(x)=2x+1+3/(x-3) is Maximum(-sqrt(3/2)+3,7-2sqrt(6)),Minimum(sqrt(3/2)+3,2sqrt(6)+7)

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

extreme points

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

Maximum (- \frac{3}{2} + 3, 7 - 26), Minimum (\frac{3}{2} + 3, 26 + 7)

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Decreasing

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

Increasing

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

Plug

x = - \frac{3}{2} + 3

into

2 x + 1 + \frac{3}{x - 3} : 7 - 26

Maximum (- \frac{3}{2} + 3, 7 - 26)

Plug

x = \frac{3}{2} + 3

into

2 x + 1 + \frac{3}{x - 3} : 26 + 7

Minimum (\frac{3}{2} + 3, 26 + 7)

Maximum (- \frac{3}{2} + 3, 7 - 26), Minimum (\frac{3}{2} + 3, 26 + 7)

f (x) = \frac{x ^{2} + 8 x - 20}{x - 6}

f (x) = x + 4 y

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

f (x) = \frac{1}{2} I n (\frac{1 + x}{1 - 1})

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

What is the extreme f(x)=2x+1+3/(x-3) ?
The extreme f(x)=2x+1+3/(x-3) is Maximum(-sqrt(3/2)+3,7-2sqrt(6)),Minimum(sqrt(3/2)+3,2sqrt(6)+7)