Limits, Continuity and Differentiability

Continuity implies differentiability

What goes wrong

Assumes a function that is continuous everywhere is automatically differentiable, ignoring sharp corners or cusp points.

Next time

Always evaluate both the left-hand derivative and right-hand derivative at the boundary point to confirm they match before declaring the function differentiable.

Questions that set this trap

1 published question

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