What is the extreme f(x)=3x+6x^{-1} ?

The extreme f(x)=3x+6x^{-1} is Maximum(-sqrt(2),-6sqrt(2)),Minimum(sqrt(2),6sqrt(2))

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extreme f(x)=3x+6x^{-1}

extreme

Maximum (- 2, - 62), Minimum (2, 62)

Solution steps

f^{'} (x) = 3 - \frac{6}{x ^{2}}

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 2

into

3 x + 6 x^{- 1} : - 62

Maximum (- 2, - 62)

Plug

x = 2

into

3 x + 6 x^{- 1} : 62

Minimum (2, 62)

Maximum (- 2, - 62), Minimum (2, 62)

What is the extreme f(x)=3x+6x^{-1} ?
The extreme f(x)=3x+6x^{-1} is Maximum(-sqrt(2),-6sqrt(2)),Minimum(sqrt(2),6sqrt(2))