Discussion
True or false: a function may have a derivative at a point without being continuous there.
Answer: C
The difference quotient \( [f(x)-f(a)]/(x-a) \) can only tend to a finite limit if the numerator tends to zero, which is continuity at \( a \). So differentiability is strictly the stronger condition, and a discontinuity of any kind, removable or not, rules the derivative out
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