What is the extreme f(x)=3x^4-4x^3-12x^2-7 ?

The extreme f(x)=3x^4-4x^3-12x^2-7 is Minimum(-1,-12),Maximum(0,-7),Minimum(2,-39)

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extreme f(x)=3x^4-4x^3-12x^2-7

extreme points

f (x) = 3 x^{4} - 4 x^{3} - 12 x^{2} - 7

Minimum (- 1, - 12), Maximum (0, - 7), Minimum (2, - 39)

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} - 7 : - 12

Minimum (- 1, - 12)

Plug

x = 0

into

3 x^{4} - 4 x^{3} - 12 x^{2} - 7 : - 7

Maximum (0, - 7)

Plug

x = 2

into

3 x^{4} - 4 x^{3} - 12 x^{2} - 7 : - 39

Minimum (2, - 39)

Minimum (- 1, - 12), Maximum (0, - 7), Minimum (2, - 39)

f (x, y) = e^{y} (4 x^{2} + 2 x y + y^{2} - 6 x - 15)

2 (x - 1)^{2} + 5

P (x y) = x^{3} y + x^{2} y - 2 x y

- 4 sin (2 π x)

f (x) = 20 + 8 x^{3} - x^{4}

What is the extreme f(x)=3x^4-4x^3-12x^2-7 ?
The extreme f(x)=3x^4-4x^3-12x^2-7 is Minimum(-1,-12),Maximum(0,-7),Minimum(2,-39)