What is the extreme f(x)=3x^4-4x^3-12x^2+5 ?

The extreme f(x)=3x^4-4x^3-12x^2+5 is Minimum(-1,0),Maximum(0,5),Minimum(2,-27)

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extreme f(x)=3x^4-4x^3-12x^2+5

extreme points

f (x) = 3 x^{4} - 4 x^{3} - 12 x^{2} + 5

Minimum (- 1, 0), Maximum (0, 5), Minimum (2, - 27)

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} + 5 : 0

Minimum (- 1, 0)

Plug

x = 0

into

3 x^{4} - 4 x^{3} - 12 x^{2} + 5 : 5

Maximum (0, 5)

Plug

x = 2

into

3 x^{4} - 4 x^{3} - 12 x^{2} + 5 : - 27

Minimum (2, - 27)

Minimum (- 1, 0), Maximum (0, 5), Minimum (2, - 27)

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

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

f (x) = 6 x^{5} - 10 x^{3}

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

f (x) = (x - 2)^{\frac{2}{3}}

What is the extreme f(x)=3x^4-4x^3-12x^2+5 ?
The extreme f(x)=3x^4-4x^3-12x^2+5 is Minimum(-1,0),Maximum(0,5),Minimum(2,-27)