alleryThe converse fails: a function with a critical point is not guaranteed to have there a:
ARemovable hole
BHorizontal shift
CLocal extremum
DVertical asymptote
Answer & Solution
Correct answer: C. Local extremum
1. Consider a curve that flattens but keeps rising.
2. Its slope is zero yet it neither peaks nor troughs.
3. So a critical point need not give a local extremum.
_Source: OpenStax Calculus Volume 1, Chapter 4, Applications of Derivatives._
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