en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme x^3-6x^2+9x+5

Solution

extreme points

x^{3} - 6 x^{2} + 9 x + 5

Solution

Maximum (1, 9), Minimum (3, 5)

Solution steps

f^{'} (x) = 3 x^{2} - 12 x + 9

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 1

into

x^{3} - 6 x^{2} + 9 x + 5 : 9

Maximum (1, 9)

Plug

x = 3

into

x^{3} - 6 x^{2} + 9 x + 5 : 5

Minimum (3, 5)

Maximum (1, 9), Minimum (3, 5)

Popular Examples

extreme f(x)=x^4-4x^3-8x^2+8 extreme points

f (x) = x^{4} - 4 x^{3} - 8 x^{2} + 8

extreme f(x,y)=6-x-2y extreme points

f (x, y) = 6 - x - 2 y

extreme 2x^3+3x^2-36x extreme points

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

extreme f(x)= 1/(\sqrt[3]{1-x^2)}extreme points

extreme f(x,y)=x^2+xy+y^2-31y+320 extreme points

f (x, y) = x^{2} + x y + y^{2} - 31 y + 320

Frequently Asked Questions (FAQ)

What is the extreme x^3-6x^2+9x+5 ?
The extreme x^3-6x^2+9x+5 is Maximum(1,9),Minimum(3,5)