What is the extreme f(x)=10+4x+9/x ?

The extreme f(x)=10+4x+9/x is Maximum(-3/2 ,-2),Minimum(3/2 ,22)

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extreme f(x)=10+4x+9/x

extreme points

f (x) = 10 + 4 x + \frac{9}{x}

Maximum (- \frac{3}{2}, - 2), Minimum (\frac{3}{2}, 22)

Solution steps

f^{'} (x) = - \frac{9}{x ^{2}} + 4

Find intervals:

Increasing

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

Decreasing

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

Decreasing

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

Increasing

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

Plug

x = - \frac{3}{2}

into

10 + 4 x + \frac{9}{x} : - 2

Maximum (- \frac{3}{2}, - 2)

Plug

x = \frac{3}{2}

into

10 + 4 x + \frac{9}{x} : 22

Minimum (\frac{3}{2}, 22)

Maximum (- \frac{3}{2}, - 2), Minimum (\frac{3}{2}, 22)

f (x) = 8 x^{3} - 17 x^{2} + 12 x + 14

f (x, y) = 3 y^{3} + 7 x y - 9 x^{2} - 5

f (x) = - \frac{cos ( 2 x )}{2} - 2 sin (x)

f (x) = e^{x^{2} - 4 x - 1}

y = e^{x} + I n x - x^{2} + \frac{3}{x ^{5}} + 3

What is the extreme f(x)=10+4x+9/x ?
The extreme f(x)=10+4x+9/x is Maximum(-3/2 ,-2),Minimum(3/2 ,22)