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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

extreme points

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

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < 5,

Decreasing

: 5 < x < \infty

Plug

x = 0

into

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

Maximum (0, 0)

Plug

x = 2

into

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

Minimum (2, - 64)

Plug

x = 5

into

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

Maximum (5, 125)

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

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