What is the extreme f(x)=27x^3-9x+1 ?

The extreme f(x)=27x^3-9x+1 is Maximum(-1/3 ,3),Minimum(1/3 ,-1)

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extreme f(x)=27x^3-9x+1

extreme points

f (x) = 27 x^{3} - 9 x + 1

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

Solution steps

f^{'} (x) = 81 x^{2} - 9

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

27 x^{3} - 9 x + 1 : 3

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

Plug

x = \frac{1}{3}

into

27 x^{3} - 9 x + 1 : - 1

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

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

What is the extreme f(x)=27x^3-9x+1 ?
The extreme f(x)=27x^3-9x+1 is Maximum(-1/3 ,3),Minimum(1/3 ,-1)