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

The extreme f(x)= 1/3 x^3-2x^2+3x is Maximum(1, 4/3),Minimum(3,0)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

extreme points

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

Maximum (1, \frac{4}{3}), Minimum (3, 0)

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 : \frac{4}{3}

Maximum (1, \frac{4}{3})

Plug

x = 3

into

\frac{1}{3} x^{3} - 2 x^{2} + 3 x : 0

Minimum (3, 0)

Maximum (1, \frac{4}{3}), Minimum (3, 0)

(1, 1), (2, 2)

y = \frac{1}{2} ∣ x + 4 ∣

lo g_{3} (x + 8)

(2, 12.5), (5, 5)

- x^{4} - 9 x^{3} + 8 x + 5

What is the extreme f(x)= 1/3 x^3-2x^2+3x ?
The extreme f(x)= 1/3 x^3-2x^2+3x is Maximum(1, 4/3),Minimum(3,0)