What is the extreme x-x^3 ?

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

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extreme x-x^3

extreme

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

Solution steps

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

Find intervals:

Decreasing

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

Increasing

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

Decreasing

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

Plug

x = - \frac{1}{3}

into

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

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

Plug

x = \frac{1}{3}

into

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

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

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

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