What is the extreme f(x)=5x+3/x ?

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

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extreme f(x)=5x+3/x

extreme points

f (x) = 5 x + \frac{3}{x}

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

Solution steps

f^{'} (x) = 5 - \frac{3}{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 + \frac{3}{x} : - 215

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

Plug

x = \frac{3}{5}

into

5 x + \frac{3}{x} : 215

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

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

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