The function is defined by q(x)= cases x, & x 0, ^ 1/3 , & x>0

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

Problem

The function qq is defined by q(x)={x,x≤0,x1/3,x>0.q(x)=\begin{cases}x, & x\leq0,\\x^{1/3}, & x>0.\end{cases} Which statement about q′(0)q'(0) is correct? (a) q′(0)q'(0) exists and equals 11 (b) q′(0)q'(0) does not exist (c) q′(0)q'(0) exists and equals 00 (d) q′(0)q'(0) exists and equals +∞+\infty

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