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6-15.

Sketch a continuous function with the following properties: , does not exist, for , and for . Homework Help ✎

Translation: the slope of is zero at . Note: is a CANDIDATE for local max or min. (It might also be a point of inflection.)

Reasons why a derivative might not exist at a point:
cusp
endpoint
jump
hole
vertical tangent

for  and for

Translation: There is a change in concavity at .