What is the extreme f(x)=x^3-27/2 x^2+42x+1 ?

The extreme f(x)=x^3-27/2 x^2+42x+1 is Maximum(2,39),Minimum(7,-47/2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=x^3-27/2 x^2+42x+1

extreme

Maximum (2, 39), Minimum (7, - \frac{47}{2})

Solution steps

f^{'} (x) = 3 x^{2} - 27 x + 42

Find intervals:

Increasing

: - \infty < x < 2,

Decreasing

: 2 < x < 7,

Increasing

: 7 < x < \infty

Plug

x = 2

into

x^{3} - \frac{27}{2} x^{2} + 42 x + 1 : 39

Maximum (2, 39)

Plug

x = 7

into

x^{3} - \frac{27}{2} x^{2} + 42 x + 1 : - \frac{47}{2}

Minimum (7, - \frac{47}{2})

Maximum (2, 39), Minimum (7, - \frac{47}{2})

What is the extreme f(x)=x^3-27/2 x^2+42x+1 ?
The extreme f(x)=x^3-27/2 x^2+42x+1 is Maximum(2,39),Minimum(7,-47/2)