What is the extreme (6|x|)/(|x-1|) ?

The extreme (6|x|)/(|x-1|) is Minimum(0,0)

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extreme (6|x|)/(|x-1|)

extreme points

\frac{6 ∣ x ∣}{∣ x - 1 ∣}

Minimum (0, 0)

Solution steps

Find the critical points:

x = 0

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug the extreme point

x = 0

into

\frac{6 ∣ x ∣}{∣ x - 1 ∣} \Rightarrow y = 0

Minimum (0, 0)

f (x) = \frac{1}{3} x^{3} - \frac{3}{2} x^{2} - 18 x + \frac{1}{3}

\frac{2 x - 6}{x + 3}

f (x, y) = x y + x^{2} + y^{2} + x - y + 17

f (x) = 4 x - 7 x^{\frac{4}{7}}

f (x) = 25 x - 25 x e^{- y} - 50 y - x^{2}