Apentix/AP Calculus AB/Unit 2: Differentiation: Definition and Basic Derivative Rules/Question
AP Calculus ABhardmcq1 pt

Which of the following functions is differentiable at x = 0?

A.C) f(x) = x^2 if x < 0, x^3 if x ≥ 0
B.A) f(x) = |x|
C.D) f(x) = x sin(1/x) if x ≠ 0, 0 if x = 0
D.B) f(x) = x^(1/3)

Explanation

Core Concept

Option A has a corner at x=0. Option B has a vertical tangent at x=0. Option D is not continuous at x=0. Option C is continuous and smooth at x=0 with matching derivatives from both sides.

Correct Answer

AC) f(x) = x^2 if x < 0, x^3 if x ≥ 0

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