What is the extreme f(x)=2x^3-36x^2+162x-4 ?

The extreme f(x)=2x^3-36x^2+162x-4 is Maximum(3,212),Minimum(9,-4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=2x^3-36x^2+162x-4

extreme

Maximum (3, 212), Minimum (9, - 4)

Solution steps

f^{'} (x) = 6 x^{2} - 72 x + 162

Find intervals:

Increasing

: - \infty < x < 3,

Decreasing

: 3 < x < 9,

Increasing

: 9 < x < \infty

Plug

x = 3

into

2 x^{3} - 36 x^{2} + 162 x - 4 : 212

Maximum (3, 212)

Plug

x = 9

into

2 x^{3} - 36 x^{2} + 162 x - 4 : - 4

Minimum (9, - 4)

Maximum (3, 212), Minimum (9, - 4)

What is the extreme f(x)=2x^3-36x^2+162x-4 ?
The extreme f(x)=2x^3-36x^2+162x-4 is Maximum(3,212),Minimum(9,-4)