What is the extreme x+(192)/x ?

The extreme x+(192)/x is Maximum(-8sqrt(3),-16sqrt(3)),Minimum(8sqrt(3),16sqrt(3))

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extreme x+(192)/x

extreme points

x + \frac{192}{x}

Maximum (- 83, - 163), Minimum (83, 163)

Solution steps

f^{'} (x) = 1 - \frac{192}{x ^{2}}

Find intervals:

Increasing

: - \infty < x < - 83,

Decreasing

: - 83 < x < 0,

Decreasing

: 0 < x < 83,

Increasing

: 83 < x < \infty

Plug

x = - 83

into

x + \frac{192}{x} : - 163

Maximum (- 83, - 163)

Plug

x = 83

into

x + \frac{192}{x} : 163

Minimum (83, 163)

Maximum (- 83, - 163), Minimum (83, 163)

f (x) = - \frac{x ^{2}}{10} + 2 x + 3

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

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

16 \cdot x - 4 \cdot ln (x)

f (x, y, z) = 64

What is the extreme x+(192)/x ?
The extreme x+(192)/x is Maximum(-8sqrt(3),-16sqrt(3)),Minimum(8sqrt(3),16sqrt(3))