Limits, Continuity and Differentiability

Non-differentiability assumed inherited by composition

What goes wrong

Assumes a composite function g(f(x)) is automatically non-differentiable wherever the inner function f(x) is non-differentiable.

Next time

Check the derivative using first principles or chain rule limits; the outer function can smooth out inner non-differentiable points.

Questions that set this trap

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No published questions for this trap yet.

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