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