What is the extreme 2x^3-2x+6 ?

The extreme 2x^3-2x+6 is Maximum(-1/(sqrt(3)), 4/(3sqrt(3))+6),Minimum(1/(sqrt(3)),-4/(3sqrt(3))+6)

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extreme 2x^3-2x+6

extreme

Maximum (- \frac{1}{3}, \frac{4}{3 3} + 6), Minimum (\frac{1}{3}, - \frac{4}{3 3} + 6)

Solution steps

f^{'} (x) = 6 x^{2} - 2

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

2 x^{3} - 2 x + 6 : \frac{4}{3 3} + 6

Maximum (- \frac{1}{3}, \frac{4}{3 3} + 6)

Plug

x = \frac{1}{3}

into

2 x^{3} - 2 x + 6 : - \frac{4}{3 3} + 6

Minimum (\frac{1}{3}, - \frac{4}{3 3} + 6)

Maximum (- \frac{1}{3}, \frac{4}{3 3} + 6), Minimum (\frac{1}{3}, - \frac{4}{3 3} + 6)

What is the extreme 2x^3-2x+6 ?
The extreme 2x^3-2x+6 is Maximum(-1/(sqrt(3)), 4/(3sqrt(3))+6),Minimum(1/(sqrt(3)),-4/(3sqrt(3))+6)