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+7

Solution

extreme points

x^{3} - 6 x^{2} + 9 x + 7

Solution

Maximum (1, 11), Minimum (3, 7)

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 + 7 : 11

Maximum (1, 11)

Plug

x = 3

into

x^{3} - 6 x^{2} + 9 x + 7 : 7

Minimum (3, 7)

Maximum (1, 11), Minimum (3, 7)

Graph

Popular Examples

extreme x^2+xy-y^2 extreme points

x^{2} + x y - y^{2}

extreme f(x)= 1/3 x^3-3x^2+5x extreme points

f (x) = \frac{1}{3} x^{3} - 3 x^{2} + 5 x

extreme f(u,v)=3u-7v extreme points

f (u, v) = 3 u - 7 v

extreme f(x)=x^4-4x^2-2 extreme points

f (x) = x^{4} - 4 x^{2} - 2

extreme sin(3X)extreme points

sin (3 X)

Frequently Asked Questions (FAQ)

What is the extreme x^3-6x^2+9x+7 ?
The extreme x^3-6x^2+9x+7 is Maximum(1,11),Minimum(3,7)