What is the extreme x^3-x+1 ?

The extreme x^3-x+1 is Maximum(-1/(sqrt(3)), 2/(3sqrt(3))+1),Minimum(1/(sqrt(3)),-2/(3sqrt(3))+1)

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extreme x^3-x+1

extreme points

x^{3} - x + 1

Maximum (- \frac{1}{3}, \frac{2}{3 3} + 1), Minimum (\frac{1}{3}, - \frac{2}{3 3} + 1)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - \frac{1}{3},

Decreasing

: - \frac{1}{3} < x < \frac{1}{3},

Increasing

: \frac{1}{3} < x < \infty

Plug

x = - \frac{1}{3}

into

x^{3} - x + 1 : \frac{2}{3 3} + 1

Maximum (- \frac{1}{3}, \frac{2}{3 3} + 1)

Plug

x = \frac{1}{3}

into

x^{3} - x + 1 : - \frac{2}{3 3} + 1

Minimum (\frac{1}{3}, - \frac{2}{3 3} + 1)

Maximum (- \frac{1}{3}, \frac{2}{3 3} + 1), Minimum (\frac{1}{3}, - \frac{2}{3 3} + 1)

f (x) = \frac{2 x}{x + 3}

y = - 2 x^{2} - 10 x

f (x) = - x

f (x) = 4 (0.76)^{x} - 2

f (x) = (x^{2} - 4)^{\frac{1}{5}}

What is the extreme x^3-x+1 ?
The extreme x^3-x+1 is Maximum(-1/(sqrt(3)), 2/(3sqrt(3))+1),Minimum(1/(sqrt(3)),-2/(3sqrt(3))+1)