What is the extreme x^3-3x^2-9x+3 ?

The extreme x^3-3x^2-9x+3 is Maximum(-1,8),Minimum(3,-24)

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extreme x^3-3x^2-9x+3

extreme points

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

Maximum (- 1, 8), Minimum (3, - 24)

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 + 3 : 8

Maximum (- 1, 8)

Plug

x = 3

into

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

Minimum (3, - 24)

Maximum (- 1, 8), Minimum (3, - 24)

f (x) = \frac{x ^{3}}{x ^{2} - 64}

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

\frac{x ^{2} - 3 x - 10}{x + 1}

f (x) = 5 x^{3} - 5 x^{2} - 5 x + 7, - 1 \leq x \leq 2

\frac{x + 6}{24 - x ^{2} - 49}

What is the extreme x^3-3x^2-9x+3 ?
The extreme x^3-3x^2-9x+3 is Maximum(-1,8),Minimum(3,-24)