What is the extreme f(x)=2+12x+3x^2-2x^3 ?

The extreme f(x)=2+12x+3x^2-2x^3 is Minimum(-1,-5),Maximum(2,22)

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extreme f(x)=2+12x+3x^2-2x^3

extreme points

f (x) = 2 + 12 x + 3 x^{2} - 2 x^{3}

Minimum (- 1, - 5), Maximum (2, 22)

Solution steps

f^{'} (x) = - 6 x^{2} + 6 x + 12

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 1

into

2 + 12 x + 3 x^{2} - 2 x^{3} : - 5

Minimum (- 1, - 5)

Plug

x = 2

into

2 + 12 x + 3 x^{2} - 2 x^{3} : 22

Maximum (2, 22)

Minimum (- 1, - 5), Maximum (2, 22)

f (x, y) = 9 - x^{2} - 9 y^{2}

f (x) = x^{4} + 2 x^{3} - 2 x^{2} + 2

f (x) = 5 - x^{2}

x^{4} - 5 x^{3}

f (x) = 4 x^{3} - 3 x^{2} - 6 x + 3, - 1 \leq x \leq 10

What is the extreme f(x)=2+12x+3x^2-2x^3 ?
The extreme f(x)=2+12x+3x^2-2x^3 is Minimum(-1,-5),Maximum(2,22)