CK12 Calculus - Single Variable

. Hencethe functionis differentiableat everypoint of its domain,
and since on its domain,then is decreasingon its domain,
.

.

in the domainof Hencethereare no relativeextremaand no inflectionpoints.

So when Hencethe graphis concaveup for

Similarly, when Hencethe graphis concavedownfor
Let’s summarizeour resultsin the tablebeforewe sketchthe graph.
Table Summary

Analysis

Domainand Range

zero at -interceptat

Interceptsand Zeros

Asymptotesand limitsat infinity VA at HA at hole in the graphat

Differentiability differentiableat everypointof its domain

Intervalswheref is increasing nowhere

Intervalswheref is decreasing

Relativeextrema none

Concavity concaveup in concavedownin

Inflectionpoints none

Finally, we sketchthe graphas follows:

Let’s look at examplesof the otherrepresentaivefunctionswe introducedin Lesson1.2.