What is the extreme 2+3x+27x^{-1} ?

The extreme 2+3x+27x^{-1} is Maximum(-3,-16),Minimum(3,20)

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extreme 2+3x+27x^{-1}

extreme points

2 + 3 x + 27 x^{- 1}

Maximum (- 3, - 16), Minimum (3, 20)

Solution steps

f^{'} (x) = - \frac{27}{x ^{2}} + 3

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 3

into

2 + 3 x + 27 x^{- 1} : - 16

Maximum (- 3, - 16)

Plug

x = 3

into

2 + 3 x + 27 x^{- 1} : 20

Minimum (3, 20)

Maximum (- 3, - 16), Minimum (3, 20)

f (x) = x^{3} - 12 x^{2} + 45 x + 2

f (x) = - 5 x^{3} - 4 x^{4}

f (x, y) = 4 x y + x^{4} + y^{4}

f (x) = x^{2} + 3 y^{2} - 2 x + 18 y

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

What is the extreme 2+3x+27x^{-1} ?
The extreme 2+3x+27x^{-1} is Maximum(-3,-16),Minimum(3,20)