MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
The function g(x)=x is defined on the closed interval [0,9]. Which of the following best describes the differentiability of g at x=0?
(a) g is differentiable at x=0 because the right-hand derivative exists and equals 0.
(b) g is differentiable at x=0 because the one-sided derivatives both exist and are equal to ∞.
(c) g is not differentiable at x=0 because the right-hand derivative is unbounded and the left-hand derivative is undefined.
(d) g is not differentiable at x=0 because the left-hand derivative is undefined even though the right-hand derivative equals 0.