What is the extreme f(x)=2x^3-9x^2-24x+9 ?

The extreme f(x)=2x^3-9x^2-24x+9 is Maximum(-1,22),Minimum(4,-103)

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extreme f(x)=2x^3-9x^2-24x+9

extreme points

f (x) = 2 x^{3} - 9 x^{2} - 24 x + 9

Maximum (- 1, 22), Minimum (4, - 103)

Solution steps

f^{'} (x) = 6 x^{2} - 18 x - 24

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = - 1

into

2 x^{3} - 9 x^{2} - 24 x + 9 : 22

Maximum (- 1, 22)

Plug

x = 4

into

2 x^{3} - 9 x^{2} - 24 x + 9 : - 103

Minimum (4, - 103)

Maximum (- 1, 22), Minimum (4, - 103)

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

\frac{1}{x ^{3} + 1}

x - 1

- x^{2} + x + 30

(1, 3), (5, 3)

What is the extreme f(x)=2x^3-9x^2-24x+9 ?
The extreme f(x)=2x^3-9x^2-24x+9 is Maximum(-1,22),Minimum(4,-103)