What is the extreme x+12x^{-1}+18x^{-2} ?

The extreme x+12x^{-1}+18x^{-2} is Minimum(4.47677…,8.05541…)

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extreme x+12x^{-1}+18x^{-2}

extreme points

x + 12 x^{- 1} + 18 x^{- 2}

Minimum (4.47677 \dots, 8.05541 \dots)

Solution steps

Find the critical points:

x \approx 4.47677 \dots

Domain of

x + 12 x^{- 1} + 18 x^{- 2} : x < 0 or x > 0

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 4.47677 \dots,

Increasing

: 4.47677 \dots < x < \infty

Plug the extreme point

x = 4.47677 \dots

into

x + 12 x^{- 1} + 18 x^{- 2} \Rightarrow y = 8.05541 \dots

Minimum (4.47677 \dots, 8.05541 \dots)

p (a, b) = \frac{3 ( \frac{600 ( a - b )}{a + b} ) + 1800}{a}

f (x) = x^{3} - 2 x^{2} - 15 x

y = x^{3} - \frac{3}{2} x^{2}

f (x) = 5 x^{2} - 8 x + 3

f (x) = - x^{3} + 9 x^{2} + 216 x + 4766

What is the extreme x+12x^{-1}+18x^{-2} ?
The extreme x+12x^{-1}+18x^{-2} is Minimum(4.47677…,8.05541…)