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

The extreme f(x)=x^3-4x^2 is Maximum(0,0),Minimum(8/3 ,-256/27)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=x^3-4x^2

extreme points

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

Maximum (0, 0), Minimum (\frac{8}{3}, - \frac{256}{27})

Solution steps

f^{'} (x) = 3 x^{2} - 8 x

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{8}{3},

Increasing

: \frac{8}{3} < x < \infty

Plug

x = 0

into

x^{3} - 4 x^{2} : 0

Maximum (0, 0)

Plug

x = \frac{8}{3}

into

x^{3} - 4 x^{2} : - \frac{256}{27}

Minimum (\frac{8}{3}, - \frac{256}{27})

Maximum (0, 0), Minimum (\frac{8}{3}, - \frac{256}{27})

x^{3} - 12 x + 3

f (x, y) = x y + \frac{3}{x} + \frac{9}{y}

\frac{4 x}{x ^{2} - 9}

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

2 x^{3} + 3 x^{2} - 180 x

What is the extreme f(x)=x^3-4x^2 ?
The extreme f(x)=x^3-4x^2 is Maximum(0,0),Minimum(8/3 ,-256/27)