What is the extreme f(x)=6x+(384)/x ?

The extreme f(x)=6x+(384)/x is Maximum(-8,-96),Minimum(8,96)

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extreme f(x)=6x+(384)/x

extreme points

f (x) = 6 x + \frac{384}{x}

Maximum (- 8, - 96), Minimum (8, 96)

Solution steps

f^{'} (x) = 6 - \frac{384}{x ^{2}}

Find intervals:

Increasing

: - \infty < x < - 8,

Decreasing

: - 8 < x < 0,

Decreasing

: 0 < x < 8,

Increasing

: 8 < x < \infty

Plug

x = - 8

into

6 x + \frac{384}{x} : - 96

Maximum (- 8, - 96)

Plug

x = 8

into

6 x + \frac{384}{x} : 96

Minimum (8, 96)

Maximum (- 8, - 96), Minimum (8, 96)

f (x) = - 2 x^{3} + 36 x^{2} - 192 x

f (x) = 2 x^{3} - 6 x^{2} - 144 x + 7

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

f (x) = x (23 - 41 + 2 x) (\frac{41}{2} - x)

x^{3} - 3 x^{2} - 9 x + 2

What is the extreme f(x)=6x+(384)/x ?
The extreme f(x)=6x+(384)/x is Maximum(-8,-96),Minimum(8,96)