en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Functions >

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

Solution

extreme

Solution

Minimum (- \frac{- 2 + 22}{6}, \frac{44 2 - 8 11}{9 11}), Maximum (\frac{2 + 22}{6}, - \frac{44 2 + 8 11}{9 11})

Solution steps

f^{'} (x) = \frac{- 12 x ^{2} + 8 x + 6}{( 1 - 3 x ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < \frac{2 - 22}{6},

Increasing

: \frac{2 - 22}{6} < x < \frac{1}{3},

Increasing

: \frac{1}{3} < x < \frac{2 + 22}{6},

Decreasing

: \frac{2 + 22}{6} < x < \infty

Plug

x = - \frac{- 2 + 22}{6}

into

\frac{2 + 4 x ^{2}}{1 - 3 x} : \frac{44 2 - 8 11}{9 11}

Minimum (- \frac{- 2 + 22}{6}, \frac{44 2 - 8 11}{9 11})

Plug

x = \frac{2 + 22}{6}

into

\frac{2 + 4 x ^{2}}{1 - 3 x} : - \frac{44 2 + 8 11}{9 11}

Maximum (\frac{2 + 22}{6}, - \frac{44 2 + 8 11}{9 11})

Minimum (- \frac{- 2 + 22}{6}, \frac{44 2 - 8 11}{9 11}), Maximum (\frac{2 + 22}{6}, - \frac{44 2 + 8 11}{9 11})

Graph

Popular Examples

extreme f(x,y)=3x-5y-2

extreme f(x)=x^3-2x^2-6x+1

extreme x^2+12+18x^{-1}

extreme f(x)=x*y*e^{x+2y}

extreme f(x)=(350)/((1+34e^{-t))}

Frequently Asked Questions (FAQ)

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