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

The extreme f(x)=2+9x+3x^2-x^3 is Minimum(-1,-3),Maximum(3,29)

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

extreme points

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

Minimum (- 1, - 3), Maximum (3, 29)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 1

into

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

Minimum (- 1, - 3)

Plug

x = 3

into

2 + 9 x + 3 x^{2} - x^{3} : 29

Maximum (3, 29)

Minimum (- 1, - 3), Maximum (3, 29)

f (x) = cos (x) - 2 x

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

y = x^{3} - 3 x^{2} - 9 x + 1

f (x) = \frac{2}{3} x^{3} + 14 x^{2} + 96 x + 7

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

What is the extreme f(x)=2+9x+3x^2-x^3 ?
The extreme f(x)=2+9x+3x^2-x^3 is Minimum(-1,-3),Maximum(3,29)