The derivative of a continuous function fails to exist at because the slopes of the…

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

The derivative of a continuous function ff fails to exist at x=ax=a because the slopes of the secant lines approaching from the left and the right are finite but unequal. Which graphical feature at x=ax=a best accounts for this failure? (a) A vertical tangent (b) A removable discontinuity (c) A sharp corner (d) A cusp

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