Limits, Continuity and Differentiability

Critical point assumed as extremum

What goes wrong

Assumes any critical point or boundary point is automatically a local extremum without verifying a sign change in the first derivative.

Next time

Check for a sign change in f′(x) or test f′′(x) to confirm it is an extremum, not an inflection point.

Questions that set this trap

3 published questions

Non-differentiability treated as discontinuity Critical points restricted to f'(x) = 0 Continuity implies differentiability Non-differentiability assumed inherited by composition