What is the extreme f(x)=-x^3+3x^2+9x-27 ?

The extreme f(x)=-x^3+3x^2+9x-27 is Minimum(-1,-32),Maximum(3,0)

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extreme f(x)=-x^3+3x^2+9x-27

extreme points

f (x) = - x^{3} + 3 x^{2} + 9 x - 27

Minimum (- 1, - 32), Maximum (3, 0)

Solution steps

f^{'} (x) = - 3 x^{2} + 6 x + 9

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 1

into

- x^{3} + 3 x^{2} + 9 x - 27 : - 32

Minimum (- 1, - 32)

Plug

x = 3

into

- x^{3} + 3 x^{2} + 9 x - 27 : 0

Maximum (3, 0)

Minimum (- 1, - 32), Maximum (3, 0)

f (x) = 2 x^{3} + 3 x^{2} - 2 x - 3

\frac{( x + 1 )}{x ^{2} - 2 x - 3}

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

f (x) = \frac{x ^{3}}{3} - 5 x^{2} - 50 x + 1

\frac{4}{x} + x^{4}

What is the extreme f(x)=-x^3+3x^2+9x-27 ?
The extreme f(x)=-x^3+3x^2+9x-27 is Minimum(-1,-32),Maximum(3,0)