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

The extreme f(x)=27x^3-9x+9 is Maximum(-1/3 ,11),Minimum(1/3 ,7)

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

extreme points

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

Maximum (- \frac{1}{3}, 11), Minimum (\frac{1}{3}, 7)

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 + 9 : 11

Maximum (- \frac{1}{3}, 11)

Plug

x = \frac{1}{3}

into

27 x^{3} - 9 x + 9 : 7

Minimum (\frac{1}{3}, 7)

Maximum (- \frac{1}{3}, 11), Minimum (\frac{1}{3}, 7)

f (x) = (9 - x^{2})^{\frac{3}{2}}

f (x) = x^{3} - 27 x + 10

(53) (5 - 8)

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

(- 1.8) (- 9.6)

What is the extreme f(x)=27x^3-9x+9 ?
The extreme f(x)=27x^3-9x+9 is Maximum(-1/3 ,11),Minimum(1/3 ,7)