What is the extreme x^3-12x^2+36x+1 ?

The extreme x^3-12x^2+36x+1 is Maximum(2,33),Minimum(6,1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme x^3-12x^2+36x+1

extreme points

x^{3} - 12 x^{2} + 36 x + 1

Maximum (2, 33), Minimum (6, 1)

Solution steps

f^{'} (x) = 3 x^{2} - 24 x + 36

Find intervals:

Increasing

: - \infty < x < 2,

Decreasing

: 2 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = 2

into

x^{3} - 12 x^{2} + 36 x + 1 : 33

Maximum (2, 33)

Plug

x = 6

into

x^{3} - 12 x^{2} + 36 x + 1 : 1

Minimum (6, 1)

Maximum (2, 33), Minimum (6, 1)

f (x) = x^{2} - 12 x + 36

f (x) = 8 x^{3} - 5

f (x) = - cos (- x) + 3

(2, - 7), (7, 3)

f (x) = \frac{10 x}{x + 3}

What is the extreme x^3-12x^2+36x+1 ?
The extreme x^3-12x^2+36x+1 is Maximum(2,33),Minimum(6,1)