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

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

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

extreme points

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

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 3

into

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

Maximum (- 3, 27)

Plug

x = 1

into

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

Minimum (1, - 5)

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

y = 9 lo g_{4} (x)

5 x^{\frac{1}{3}} - 6

\frac{x ^{2} - 1}{x}

f (x) = - \frac{1}{5} x + 9

x - 3

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