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

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

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

extreme

Maximum (- 1, - 10), Minimum (1, 10)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

5 x + 5 x^{- 1} : - 10

Maximum (- 1, - 10)

Plug

x = 1

into

5 x + 5 x^{- 1} : 10

Minimum (1, 10)

Maximum (- 1, - 10), Minimum (1, 10)

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