What is the extreme f(x)=-x-((64)/x) ?

The extreme f(x)=-x-((64)/x) is Minimum(-8,16),Maximum(8,-16)

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extreme f(x)=-x-((64)/x)

extreme points

f (x) = - x - (\frac{64}{x})

Minimum (- 8, 16), Maximum (8, - 16)

Solution steps

f^{'} (x) = - 1 + \frac{64}{x ^{2}}

Find intervals:

Decreasing

: - \infty < x < - 8,

Increasing

: - 8 < x < 0,

Increasing

: 0 < x < 8,

Decreasing

: 8 < x < \infty

Plug

x = - 8

into

- x - \frac{64}{x} : 16

Minimum (- 8, 16)

Plug

x = 8

into

- x - \frac{64}{x} : - 16

Maximum (8, - 16)

Minimum (- 8, 16), Maximum (8, - 16)

What is the extreme f(x)=-x-((64)/x) ?
The extreme f(x)=-x-((64)/x) is Minimum(-8,16),Maximum(8,-16)