What is the extreme f(x)=3x^4-12x^3-60x^2+4 ?

The extreme f(x)=3x^4-12x^3-60x^2+4 is Minimum(-2,-92),Maximum(0,4),Minimum(5,-1121)

extreme f(x)=3x^4-12x^3-60x^2+4

extreme points

f (x) = 3 x^{4} - 12 x^{3} - 60 x^{2} + 4

Minimum (- 2, - 92), Maximum (0, 4), Minimum (5, - 1121)

Solution steps

f^{'} (x) = 12 x^{3} - 36 x^{2} - 120 x

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 0,

Decreasing

: 0 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = - 2

into

3 x^{4} - 12 x^{3} - 60 x^{2} + 4 : - 92

Minimum (- 2, - 92)

Plug

x = 0

into

3 x^{4} - 12 x^{3} - 60 x^{2} + 4 : 4

Maximum (0, 4)

Plug

x = 5

into

3 x^{4} - 12 x^{3} - 60 x^{2} + 4 : - 1121

Minimum (5, - 1121)

Minimum (- 2, - 92), Maximum (0, 4), Minimum (5, - 1121)

f (x) = 13 e^{- x}

f (x) = - x^{4} - 6 x

P (X, Y) = 36 X^{2} - 9 Y^{2}

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

\frac{4}{x}

What is the extreme f(x)=3x^4-12x^3-60x^2+4 ?
The extreme f(x)=3x^4-12x^3-60x^2+4 is Minimum(-2,-92),Maximum(0,4),Minimum(5,-1121)