What is the extreme F(x)=3x^4-4x^3-12x^2+2 ?

The extreme F(x)=3x^4-4x^3-12x^2+2 is Minimum(-1,-3),Maximum(0,2),Minimum(2,-30)

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extreme F(x)=3x^4-4x^3-12x^2+2

extreme points

F (x) = 3 x^{4} - 4 x^{3} - 12 x^{2} + 2

Minimum (- 1, - 3), Maximum (0, 2), Minimum (2, - 30)

Solution steps

f^{'} (x) = 12 x^{3} - 12 x^{2} - 24 x

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 1

into

3 x^{4} - 4 x^{3} - 12 x^{2} + 2 : - 3

Minimum (- 1, - 3)

Plug

x = 0

into

3 x^{4} - 4 x^{3} - 12 x^{2} + 2 : 2

Maximum (0, 2)

Plug

x = 2

into

3 x^{4} - 4 x^{3} - 12 x^{2} + 2 : - 30

Minimum (2, - 30)

Minimum (- 1, - 3), Maximum (0, 2), Minimum (2, - 30)

x^{2} + 6 x + 5

f (x, y) = \frac{1}{( 1 + x \cdot y )}

0.6 \cdot (x^{4}) - 0.3 \cdot (x^{3}) - 3 \cdot (x^{2}) + 2 \cdot x

f (x) = 3 x^{4} - 8 x^{3} + 6 x^{2} + 3

f (x) = x^{3} - 4 x^{2} - 16 x - 5

What is the extreme F(x)=3x^4-4x^3-12x^2+2 ?
The extreme F(x)=3x^4-4x^3-12x^2+2 is Minimum(-1,-3),Maximum(0,2),Minimum(2,-30)