What is the extreme f(x)=16-4x-4/x ,[0,infinity ] ?

The extreme f(x)=16-4x-4/x ,[0,infinity ] is Maximum(1,8)

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extreme f(x)=16-4x-4/x ,[0,infinity ]

extreme points

f (x) = 16 - 4 x - \frac{4}{x}, [0, \infty]

Maximum (1, 8)

Solution steps

Find the critical points:

x = 1

Domain of

16 - 4 x - \frac{4}{x}, [0, \infty] : x > 0

Find intervals:

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug the extreme point

x = 1

into

16 - 4 x - \frac{4}{x} \Rightarrow y = 8

Maximum (1, 8)

f (x) = - 7 x - 6

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

f (x) = - 6 x^{2} + 84 x + 1000

f (x) = \frac{4 x}{x ^{2} + 1}, - 3 \leq x \leq 3

f (x) = \frac{4 x}{x ^{2} + 1}, - 3 \leq x \leq 0

What is the extreme f(x)=16-4x-4/x ,[0,infinity ] ?
The extreme f(x)=16-4x-4/x ,[0,infinity ] is Maximum(1,8)