What is the extreme f(x)=x^3-12x^2-27x+2,1<= x<= 10 ?

The extreme f(x)=x^3-12x^2-27x+2,1<= x<= 10 is Maximum(1,-36),Minimum(9,-484),Maximum(10,-468)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=x^3-12x^2-27x+2,1<= x<= 10

extreme points

f (x) = x^{3} - 12 x^{2} - 27 x + 2, 1 \leq x \leq 10

Maximum (1, - 36), Minimum (9, - 484), Maximum (10, - 468)

Solution steps

Find the critical points:

x = 1, x = 9, x = 10

Domain of

x^{3} - 12 x^{2} - 27 x + 2, 1 \leq x \leq 10 : 1 \leq x \leq 10

Find intervals:

Decreasing

: 1 < x < 9,

Increasing

: 9 < x < 10

Plug the extreme point

x = 1

into

x^{3} - 12 x^{2} - 27 x + 2 \Rightarrow y = - 36

Maximum (1, - 36)

Plug the extreme point

x = 9

into

x^{3} - 12 x^{2} - 27 x + 2 \Rightarrow y = - 484

Minimum (9, - 484)

Plug the extreme point

x = 10

into

x^{3} - 12 x^{2} - 27 x + 2 \Rightarrow y = - 468

Maximum (10, - 468)

Maximum (1, - 36), Minimum (9, - 484), Maximum (10, - 468)

85 y^{35}

2 x^{3} + 9 x^{2} - 24 x

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

f (x) = x^{3} - x^{2} - x - 5

f (x, y) = 3 x^{2} + 3 y - y^{3}

What is the extreme f(x)=x^3-12x^2-27x+2,1<= x<= 10 ?
The extreme f(x)=x^3-12x^2-27x+2,1<= x<= 10 is Maximum(1,-36),Minimum(9,-484),Maximum(10,-468)