Concept:Use the definition of derivative: f′(0)=limh→0hf(0+h)−f(0).Explanation:f(x)=∣x∣3, so f(0)=0.f′(0)=limh→0h∣h∣3.For h>0, ∣h∣3=h3, so hh3=h2→0.For h<0, ∣h∣3=(−h)3=−h3, so h−h3=−h2→0.Since both one-sided limits are 0, f′(0)=0.Answer:f′(0)=0, which corresponds to option B.