What is the extreme y=x^3-3x^2-9x ?

The extreme y=x^3-3x^2-9x is Maximum(-1,5),Minimum(3,-27)

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extreme y=x^3-3x^2-9x

extreme points

y = x^{3} - 3 x^{2} - 9 x

Maximum (- 1, 5), Minimum (3, - 27)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 1

into

x^{3} - 3 x^{2} - 9 x : 5

Maximum (- 1, 5)

Plug

x = 3

into

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

Minimum (3, - 27)

Maximum (- 1, 5), Minimum (3, - 27)

f (x) = x e^{- 2 x^{2} - 2 y^{2}}

f (z) = z + z^{3} - 2 z^{2} - 4

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

f (x) = \frac{x ^{2} - 0.8 x + 0.32}{1.6 - 2 x}

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

What is the extreme y=x^3-3x^2-9x ?
The extreme y=x^3-3x^2-9x is Maximum(-1,5),Minimum(3,-27)