What is the extreme g(x)=x^3-9x^2+15x+2 ?

The extreme g(x)=x^3-9x^2+15x+2 is Maximum(1,9),Minimum(5,-23)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme g(x)=x^3-9x^2+15x+2

extreme points

g (x) = x^{3} - 9 x^{2} + 15 x + 2

Maximum (1, 9), Minimum (5, - 23)

Solution steps

f^{'} (x) = 3 x^{2} - 18 x + 15

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = 1

into

x^{3} - 9 x^{2} + 15 x + 2 : 9

Maximum (1, 9)

Plug

x = 5

into

x^{3} - 9 x^{2} + 15 x + 2 : - 23

Minimum (5, - 23)

Maximum (1, 9), Minimum (5, - 23)

What is the extreme g(x)=x^3-9x^2+15x+2 ?
The extreme g(x)=x^3-9x^2+15x+2 is Maximum(1,9),Minimum(5,-23)