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

The extreme f(x)=x+6/x is Maximum(-sqrt(6),-2sqrt(6)),Minimum(sqrt(6),2sqrt(6))

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extreme f(x)=x+6/x

extreme

Maximum (- 6, - 26), Minimum (6, 26)

Solution steps

f^{'} (x) = 1 - \frac{6}{x ^{2}}

Find intervals:

Increasing

: - \infty < x < - 6,

Decreasing

: - 6 < x < 0,

Decreasing

: 0 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = - 6

into

x + \frac{6}{x} : - 26

Maximum (- 6, - 26)

Plug

x = 6

into

x + \frac{6}{x} : 26

Minimum (6, 26)

Maximum (- 6, - 26), Minimum (6, 26)

What is the extreme f(x)=x+6/x ?
The extreme f(x)=x+6/x is Maximum(-sqrt(6),-2sqrt(6)),Minimum(sqrt(6),2sqrt(6))