MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
Let
h(x)={kx2,kx,x<0,x≥0,
where k=0 is a constant. Which statement about the differentiability of h at x=0 is correct?
(a) h is differentiable at x=0 for every nonzero k because both one-sided derivatives are 0.
(b) h is not differentiable at x=0 for any nonzero k because the left-hand derivative is 0 while the right-hand derivative is k.
(c) h is differentiable at x=0 only when k=1.
(d) h is differentiable at x=0 for every nonzero k because both pieces are polynomials and therefore smooth.