What is the extreme f(x)=2x+(32)/x ?

The extreme f(x)=2x+(32)/x is Maximum(-4,-16),Minimum(4,16)

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extreme f(x)=2x+(32)/x

extreme points

f (x) = 2 x + \frac{32}{x}

Maximum (- 4, - 16), Minimum (4, 16)

Solution steps

f^{'} (x) = 2 - \frac{32}{x ^{2}}

Find intervals:

Increasing

: - \infty < x < - 4,

Decreasing

: - 4 < x < 0,

Decreasing

: 0 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = - 4

into

2 x + \frac{32}{x} : - 16

Maximum (- 4, - 16)

Plug

x = 4

into

2 x + \frac{32}{x} : 16

Minimum (4, 16)

Maximum (- 4, - 16), Minimum (4, 16)

f (x) = \frac{x ^{3}}{3} - x^{2} - 3 x - 1, - 7 \leq x \leq 7

y = (x - 4)^{4} (x + 3)^{3}

- x^{3} + 6 x^{2}

f (x) = 6 x^{3} - 21 x^{2} + 36 x - 5

f (x) = \frac{1}{3} x^{3} - 2 x^{2} - 5 x - 10

What is the extreme f(x)=2x+(32)/x ?
The extreme f(x)=2x+(32)/x is Maximum(-4,-16),Minimum(4,16)