What is the extreme f(x)=3x^4-4x^3-12x^2+1[-2.3] ?

The extreme f(x)=3x^4-4x^3-12x^2+1[-2.3] is Minimum(-1,-7.3),Maximum(0,-2.3),Minimum(2,-34.3)

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extreme f(x)=3x^4-4x^3-12x^2+1[-2.3]

extreme

Minimum (- 1, - 7.3), Maximum (0, - 2.3), Minimum (2, - 34.3)

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} + 1 [- 2.3] : - 7.3

Minimum (- 1, - 7.3)

Plug

x = 0

into

3 x^{4} - 4 x^{3} - 12 x^{2} + 1 [- 2.3] : - 2.3

Maximum (0, - 2.3)

Plug

x = 2

into

3 x^{4} - 4 x^{3} - 12 x^{2} + 1 [- 2.3] : - 34.3

Minimum (2, - 34.3)

Minimum (- 1, - 7.3), Maximum (0, - 2.3), Minimum (2, - 34.3)

What is the extreme f(x)=3x^4-4x^3-12x^2+1[-2.3] ?
The extreme f(x)=3x^4-4x^3-12x^2+1[-2.3] is Minimum(-1,-7.3),Maximum(0,-2.3),Minimum(2,-34.3)