What is the extreme f(x)=5x+2x^{-1} ?

The extreme f(x)=5x+2x^{-1} is Maximum(-sqrt(2/5),-2sqrt(10)),Minimum(sqrt(2/5),2sqrt(10))

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extreme f(x)=5x+2x^{-1}

extreme points

f (x) = 5 x + 2 x^{- 1}

Maximum (- \frac{2}{5}, - 210), Minimum (\frac{2}{5}, 210)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - \frac{2}{5},

Decreasing

: - \frac{2}{5} < x < 0,

Decreasing

: 0 < x < \frac{2}{5},

Increasing

: \frac{2}{5} < x < \infty

Plug

x = - \frac{2}{5}

into

5 x + 2 x^{- 1} : - 210

Maximum (- \frac{2}{5}, - 210)

Plug

x = \frac{2}{5}

into

5 x + 2 x^{- 1} : 210

Minimum (\frac{2}{5}, 210)

Maximum (- \frac{2}{5}, - 210), Minimum (\frac{2}{5}, 210)

What is the extreme f(x)=5x+2x^{-1} ?
The extreme f(x)=5x+2x^{-1} is Maximum(-sqrt(2/5),-2sqrt(10)),Minimum(sqrt(2/5),2sqrt(10))