What is the extreme f(x)=-27x^3+9x+6 ?

The extreme f(x)=-27x^3+9x+6 is Minimum(-1/3 ,4),Maximum(1/3 ,8)

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extreme f(x)=-27x^3+9x+6

extreme points

f (x) = - 27 x^{3} + 9 x + 6

Minimum (- \frac{1}{3}, 4), Maximum (\frac{1}{3}, 8)

Solution steps

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

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

- 27 x^{3} + 9 x + 6 : 4

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

Plug

x = \frac{1}{3}

into

- 27 x^{3} + 9 x + 6 : 8

Maximum (\frac{1}{3}, 8)

Minimum (- \frac{1}{3}, 4), Maximum (\frac{1}{3}, 8)

\frac{x - 4}{x ^{3} - 5 x ^{2} + 12 x - 33}

f (x) = lo g_{2} (- x - 1) + 3

f (x) = 4 - x + 1

f (x) = x - 2 + 3

What is the extreme f(x)=-27x^3+9x+6 ?
The extreme f(x)=-27x^3+9x+6 is Minimum(-1/3 ,4),Maximum(1/3 ,8)