What is the extreme f(x)=5x+9x^{-1} ?

The extreme f(x)=5x+9x^{-1} is Maximum(-3/(sqrt(5)),-6sqrt(5)),Minimum(3/(sqrt(5)),6sqrt(5))

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extreme f(x)=5x+9x^{-1}

extreme

Maximum (- \frac{3}{5}, - 65), Minimum (\frac{3}{5}, 65)

Solution steps

f^{'} (x) = 5 - \frac{9}{x ^{2}}

Find intervals:

Increasing

: - \infty < x < - \frac{3}{5},

Decreasing

: - \frac{3}{5} < x < 0,

Decreasing

: 0 < x < \frac{3}{5},

Increasing

: \frac{3}{5} < x < \infty

Plug

x = - \frac{3}{5}

into

5 x + 9 x^{- 1} : - 65

Maximum (- \frac{3}{5}, - 65)

Plug

x = \frac{3}{5}

into

5 x + 9 x^{- 1} : 65

Minimum (\frac{3}{5}, 65)

Maximum (- \frac{3}{5}, - 65), Minimum (\frac{3}{5}, 65)

What is the extreme f(x)=5x+9x^{-1} ?
The extreme f(x)=5x+9x^{-1} is Maximum(-3/(sqrt(5)),-6sqrt(5)),Minimum(3/(sqrt(5)),6sqrt(5))