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

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

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+3x^2

extreme points

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

Minimum (0, 0), Maximum (2, 4)

Solution steps

f^{'} (x) = - 3 x^{2} + 6 x

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = 0

into

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

Minimum (0, 0)

Plug

x = 2

into

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

Maximum (2, 4)

Minimum (0, 0), Maximum (2, 4)

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

f (x, y) = 2 x y - 5 x^{2} - 2 y^{2} + 18 y - 8

f (x) = (x + 1)^{\frac{2}{3}} (x - 3)^{2}

f (x) = \frac{1}{4} x^{4} + \frac{4}{3} x^{3} + 2 x^{2}

f (x) = (1 - x^{2})^{2}

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