What is the extreme f(x)=-3x^4+16x^3-18x^2 ?

The extreme f(x)=-3x^4+16x^3-18x^2 is Maximum(0,0),Minimum(1,-5),Maximum(3,27)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=-3x^4+16x^3-18x^2

extreme points

f (x) = - 3 x^{4} + 16 x^{3} - 18 x^{2}

Maximum (0, 0), Minimum (1, - 5), Maximum (3, 27)

Solution steps

f^{'} (x) = - 12 x^{3} + 48 x^{2} - 36 x

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = 0

into

- 3 x^{4} + 16 x^{3} - 18 x^{2} : 0

Maximum (0, 0)

Plug

x = 1

into

- 3 x^{4} + 16 x^{3} - 18 x^{2} : - 5

Minimum (1, - 5)

Plug

x = 3

into

- 3 x^{4} + 16 x^{3} - 18 x^{2} : 27

Maximum (3, 27)

Maximum (0, 0), Minimum (1, - 5), Maximum (3, 27)

f (x) = \frac{1}{9 - x}

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

f (x) = x - 3 - 1

f (x) = 4 - x

f (x) = - 2 x

What is the extreme f(x)=-3x^4+16x^3-18x^2 ?
The extreme f(x)=-3x^4+16x^3-18x^2 is Maximum(0,0),Minimum(1,-5),Maximum(3,27)