(a) Is every function that is differentiable at a point necessarily continuous there?…

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

(a) Is every function that is differentiable at a point necessarily continuous there? Give a brief reason. (b) Let f(x)=∣x∣f(x)=|x|. (i) Examine the continuity of ff at x=0x=0. (ii) Determine whether ff is differentiable at x=0x=0, showing all necessary steps.

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