MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
Consider p(x)=∣x∣2/3. Which statement about p′(0) is true?
(a) p′(0)=0 because the graph is symmetric about the y-axis.
(b) p′(0) does not exist because the one-sided derivatives are equal and both approach +∞.
(c) p′(0) does not exist because the left-hand derivative approaches −∞ while the right-hand derivative approaches +∞.
(d) p′(0)=∞ since 32∣0∣−1/3 is unbounded, so the derivative exists and equals +∞.