{{ tocSubheader }}

{{ 'ml-label-loading-course' | message }}

{{ tocSubheader }}

{{ 'ml-toc-proceed-mlc' | message }}

{{ 'ml-toc-proceed-tbs' | message }}

An error ocurred, try again later!

Chapter {{ article.chapter.number }}

{{ article.number }}. # {{ article.displayTitle }}

{{ article.intro.summary }}

Show less Show more Lesson Settings & Tools

| {{ 'ml-lesson-number-slides' | message : article.intro.bblockCount }} |

| {{ 'ml-lesson-number-exercises' | message : article.intro.exerciseCount }} |

| {{ 'ml-lesson-time-estimation' | message }} |

Concept

Any points where a function has a maximum or a minimum are not included in either interval. The previous applet shows a function that contains two increasing intervals and one decreasing interval. Each can be described in terms of the $x-$values.

$From left side tox=-2Fromx=-2tox=0Fromx=0to right side →→→ IncreasingDecreasingIncreasing $

Although the entire graph cannot be seen, it is reasonable to assume that it continues in the same manner. In that case, for all $x-$values less than $x=-2,$ $f$ will be increasing. For all $x$-values greater than $x=0,$ $f$ will also be increasing.
$Increasing Intervals:-∞0Decreasing Interval:-2 <x<-2<x<∞<x<0 $

The point where a function switches between decreasing and increasing is known as a turning point.
Loading content