What is the extreme f(x)=3x+5x^{-1} ?

The extreme f(x)=3x+5x^{-1} is Maximum(-sqrt(5/3),-2sqrt(15)),Minimum(sqrt(5/3),2sqrt(15))

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extreme f(x)=3x+5x^{-1}

extreme points

f (x) = 3 x + 5 x^{- 1}

Maximum (- \frac{5}{3}, - 215), Minimum (\frac{5}{3}, 215)

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Decreasing

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

Increasing

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

Plug

x = - \frac{5}{3}

into

3 x + 5 x^{- 1} : - 215

Maximum (- \frac{5}{3}, - 215)

Plug

x = \frac{5}{3}

into

3 x + 5 x^{- 1} : 215

Minimum (\frac{5}{3}, 215)

Maximum (- \frac{5}{3}, - 215), Minimum (\frac{5}{3}, 215)

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

f (x, y) = 3 x y - 2 x^{3} y^{3}

f (x) = x^{2} = - 4 a y

- x^{2} - 4 y^{2} + 8 x - 8 y - 16

f (x) = (x - 1)^{2} + y^{2} = 25

What is the extreme f(x)=3x+5x^{-1} ?
The extreme f(x)=3x+5x^{-1} is Maximum(-sqrt(5/3),-2sqrt(15)),Minimum(sqrt(5/3),2sqrt(15))