What is the extreme f(x)=8x^3-6x+6 ?

The extreme f(x)=8x^3-6x+6 is Maximum(-1/2 ,8),Minimum(1/2 ,4)

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extreme f(x)=8x^3-6x+6

extreme points

f (x) = 8 x^{3} - 6 x + 6

Maximum (- \frac{1}{2}, 8), Minimum (\frac{1}{2}, 4)

Solution steps

f^{'} (x) = 24 x^{2} - 6

Find intervals:

Increasing

: - \infty < x < - \frac{1}{2},

Decreasing

: - \frac{1}{2} < x < \frac{1}{2},

Increasing

: \frac{1}{2} < x < \infty

Plug

x = - \frac{1}{2}

into

8 x^{3} - 6 x + 6 : 8

Maximum (- \frac{1}{2}, 8)

Plug

x = \frac{1}{2}

into

8 x^{3} - 6 x + 6 : 4

Minimum (\frac{1}{2}, 4)

Maximum (- \frac{1}{2}, 8), Minimum (\frac{1}{2}, 4)

What is the extreme f(x)=8x^3-6x+6 ?
The extreme f(x)=8x^3-6x+6 is Maximum(-1/2 ,8),Minimum(1/2 ,4)