What is the extreme f(x)= 1/(x^2-x-6) ?

The extreme f(x)= 1/(x^2-x-6) is Maximum(1/2 ,-4/25)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)= 1/(x^2-x-6)

extreme

Maximum (\frac{1}{2}, - \frac{4}{25})

Solution steps

f^{'} (x) = - \frac{2 x - 1}{( x ^{2} - x - 6 ) ^{2}}

Find intervals:

Increasing

: - \infty < x < - 2,

Increasing

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

Decreasing

: \frac{1}{2} < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = \frac{1}{2}

into

\frac{1}{x ^{2} - x - 6} : - \frac{4}{25}

Maximum (\frac{1}{2}, - \frac{4}{25})

What is the extreme f(x)= 1/(x^2-x-6) ?
The extreme f(x)= 1/(x^2-x-6) is Maximum(1/2 ,-4/25)