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

The extreme f(x)=2x^3-36x^2+162x+3 is Maximum(3,219),Minimum(9,3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

extreme points

f (x) = 2 x^{3} - 36 x^{2} + 162 x + 3

Maximum (3, 219), Minimum (9, 3)

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 + 3 : 219

Maximum (3, 219)

Plug

x = 9

into

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

Minimum (9, 3)

Maximum (3, 219), Minimum (9, 3)

(x + 1)^{2} (x - 2)

f (x) = x^{5} - 5 x^{4} + 5

f (x) = x^{2} + y^{2} + 8 x - 12 y - 7

4 x^{3} - 48 x - 6

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

What is the extreme f(x)=2x^3-36x^2+162x+3 ?
The extreme f(x)=2x^3-36x^2+162x+3 is Maximum(3,219),Minimum(9,3)