What is the extreme f(x)=6x+4x^{-1} ?

The extreme f(x)=6x+4x^{-1} is Maximum(-sqrt(2/3),-4sqrt(6)),Minimum(sqrt(2/3),4sqrt(6))

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extreme f(x)=6x+4x^{-1}

extreme points

f (x) = 6 x + 4 x^{- 1}

Maximum (- \frac{2}{3}, - 46), Minimum (\frac{2}{3}, 46)

Solution steps

f^{'} (x) = 6 - \frac{4}{x ^{2}}

Find intervals:

Increasing

: - \infty < x < - \frac{2}{3},

Decreasing

: - \frac{2}{3} < x < 0,

Decreasing

: 0 < x < \frac{2}{3},

Increasing

: \frac{2}{3} < x < \infty

Plug

x = - \frac{2}{3}

into

6 x + 4 x^{- 1} : - 46

Maximum (- \frac{2}{3}, - 46)

Plug

x = \frac{2}{3}

into

6 x + 4 x^{- 1} : 46

Minimum (\frac{2}{3}, 46)

Maximum (- \frac{2}{3}, - 46), Minimum (\frac{2}{3}, 46)

f (x) = - 3 x^{3} + 81 x + 9

f (x) = x^{\frac{5}{3}} - 6 x^{\frac{2}{3}}

f (r, s) = \frac{2 r}{r ^{4} + 7 s}

f (x) = 1 + \frac{7}{x} - \frac{2}{x ^{2}}

f (x) = x^{\frac{1}{3}} (x + 3)^{\frac{2}{3}}

What is the extreme f(x)=6x+4x^{-1} ?
The extreme f(x)=6x+4x^{-1} is Maximum(-sqrt(2/3),-4sqrt(6)),Minimum(sqrt(2/3),4sqrt(6))