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

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

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

extreme points

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

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

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 3

into

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

Minimum (- 3, - 24)

Plug

x = 1

into

3 + 9 x - 3 x^{2} - x^{3} : 8

Maximum (1, 8)

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

f (x) = \frac{1 - x}{x + 2}

f (x) = - \frac{10}{3} x^{3} - 19 x^{2} - 24 x + 50

y = 4 cos (\frac{x}{2}) + 2

K (r, s) = 5 r - s

f (x) = sin (x) cos (x), 0 \leq x \leq 2 π

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