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

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

Popular >

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

extreme points

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

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

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Decreasing

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

Increasing

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

Plug

x = - \frac{5}{2}

into

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

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

Plug

x = \frac{5}{2}

into

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

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

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

a - \frac{ab}{( a + b )}

f (x) = (x - 2) (x - 3)^{\frac{1}{2}}

f (x) = x^{2} + 9, - 1 \leq x \leq 4

f (x) = x (20 - 2 x) (16 - x), 0 < x < 10

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

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