CK12 Calculus - Single Variable

everywherein .Hence isconcavedownin

is not definedat , so is an absoluteminimum.
Table Summary

Analysis

Domainand Range

zerosat , no -intercept

Interceptsand Zeros

Asymptotesand limitsat infinity no asymptotes

differentiablein

Differentiability

everywherein

Intervalswheref is increasing

Intervalswheref is decreasing nowhere

Relativeextrema none

absoluteminimumat , locatedat

concavedownin

Concavity

Inflectionpoints none

Hereis a sketchof the graph:

Example4:AnalyzingTrigonometricFunctions
We will see that whiletrigonometricfunctionscan be analyzedusingwhatwe knowaboutderivatives,they
will provide some interesting challenges that we will need to address. Consider the function