CK12 Calculus - Single Variable

on the interval
GeneralProperties

We note that is a continuousfunctionand thus attainsan absolutemaximumand minimumin
Its domainis and its rangeis
Differentiability

at.

Notethat on and ; thereforethe functionis increasingin and

.

Notethat on ; thereforethe functionis decreasingin.

if Hencethe criticalvaluesare at

hencethereis a relativeminimumat

; hencethereis a relativemaximumat

on and on Hencethe graphis concaveup and decreasingon

and concavedownon Thereis an inflectionpointat locatedat the point

Finally, thereis absoluteminimumat locatedat and an absolutemaximumat
locatedat
Table Summary

Analysis

Domainand Range

Interceptsand Zeros

Asymptotesand limitsat infinity no asymptotes

Differentiability differentiablein

and

Intervalswheref is increasing