What is the extreme f(x)=3x^4-28x^3+60x^2 ?

The extreme f(x)=3x^4-28x^3+60x^2 is Minimum(0,0),Maximum(2,64),Minimum(5,-125)

extreme f(x)=3x^4-28x^3+60x^2

extreme points

f (x) = 3 x^{4} - 28 x^{3} + 60 x^{2}

Minimum (0, 0), Maximum (2, 64), Minimum (5, - 125)

Solution steps

f^{'} (x) = 12 x^{3} - 84 x^{2} + 120 x

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = 0

into

3 x^{4} - 28 x^{3} + 60 x^{2} : 0

Minimum (0, 0)

Plug

x = 2

into

3 x^{4} - 28 x^{3} + 60 x^{2} : 64

Maximum (2, 64)

Plug

x = 5

into

3 x^{4} - 28 x^{3} + 60 x^{2} : - 125

Minimum (5, - 125)

Minimum (0, 0), Maximum (2, 64), Minimum (5, - 125)

d i s t an ce (2, 7), (8, 9)

d i s t an ce (6, - 5), (- 1, - 4)

in v erse f (x) = (x + 1)^{2} + 4

in v erse f (x) = \frac{5 x}{x - 6}

in v erse 3 x^{3}

What is the extreme f(x)=3x^4-28x^3+60x^2 ?
The extreme f(x)=3x^4-28x^3+60x^2 is Minimum(0,0),Maximum(2,64),Minimum(5,-125)