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

The extreme f(x)=(x^3)/3-x^2-3x-1 is Maximum(-1, 2/3),Minimum(3,-10)

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)/3-x^2-3x-1

extreme points

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

Maximum (- 1, \frac{2}{3}), Minimum (3, - 10)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 1

into

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

Maximum (- 1, \frac{2}{3})

Plug

x = 3

into

\frac{x ^{3}}{3} - x^{2} - 3 x - 1 : - 10

Minimum (3, - 10)

Maximum (- 1, \frac{2}{3}), Minimum (3, - 10)

f (x, y) = x^{4} + y^{4} - 16 x y

f (x) = x e^{\frac{- x ^{2}}{162}}

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

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

What is the extreme f(x)=(x^3)/3-x^2-3x-1 ?
The extreme f(x)=(x^3)/3-x^2-3x-1 is Maximum(-1, 2/3),Minimum(3,-10)