What is the extreme f(x)= 1/3 x^3-2x^2+3x-4 ?

The extreme f(x)= 1/3 x^3-2x^2+3x-4 is Maximum(1,-8/3),Minimum(3,-4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)= 1/3 x^3-2x^2+3x-4

extreme points

f (x) = \frac{1}{3} x^{3} - 2 x^{2} + 3 x - 4

Maximum (1, - \frac{8}{3}), Minimum (3, - 4)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 1

into

\frac{1}{3} x^{3} - 2 x^{2} + 3 x - 4 : - \frac{8}{3}

Maximum (1, - \frac{8}{3})

Plug

x = 3

into

\frac{1}{3} x^{3} - 2 x^{2} + 3 x - 4 : - 4

Minimum (3, - 4)

Maximum (1, - \frac{8}{3}), Minimum (3, - 4)

What is the extreme f(x)= 1/3 x^3-2x^2+3x-4 ?
The extreme f(x)= 1/3 x^3-2x^2+3x-4 is Maximum(1,-8/3),Minimum(3,-4)