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

The extreme (2x^3)/3-x^2+x/2+1/3 is Saddle(1/2 , 5/12)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

extreme points

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

Saddle (\frac{1}{2}, \frac{5}{12})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < \frac{1}{2},

Increasing

: \frac{1}{2} < x < \infty

Plug

x = \frac{1}{2}

into

\frac{2 x ^{3}}{3} - x^{2} + \frac{x}{2} + \frac{1}{3} : \frac{5}{12}

Saddle (\frac{1}{2}, \frac{5}{12})

y = \frac{2}{x}

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

f (x) = 2 x - 7

- \frac{1}{2} x + 3

\frac{( x + 2 ) ^{2}}{9} - \frac{( y - 2 ) ^{2}}{16} = 1

What is the extreme (2x^3)/3-x^2+x/2+1/3 ?
The extreme (2x^3)/3-x^2+x/2+1/3 is Saddle(1/2 , 5/12)