Example8:
Finddy/dxfor
Solution:
Example9:
At whichpoint(s)doesthe graphof havea horizontaltangentline?
Solution:
Sincethe slopeof a horizontalline is zero,and sincethe derivativeof a functionsignifiesthe slopeof the
tangentline, then takingthe derivativeand equatingit to zero will enableus to find the pointsat whichthe
slopeof the tangentline equalsto zero,i.e., the locationsof the horizontaltangents.
Multiplyingby the denominatorand solvingforx,
Thereforethe tangentline is horizontalat
HigherDerivatives
If the derivativefof the functionf is differentiable,thenthe derivativeof f, denotedby f" , is calledthe
secondderivativeof f. We can continuethe processof differentiatingderivativesand obtainthird,