MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
The function g(x)=∣x∣ is continuous at x=0, but g′(0) does not exist. Which of the following best explains the absence of the derivative at x=0?
(a) The tangent line to g at x=0 is horizontal, giving a slope of 0.},{
(b) x→0limx−0g(x)−g(0) is infinite.
(c) The left-hand and right-hand limits of x−0g(x)−g(0) are not equal as x→0.},{
(d) The left-hand and right-hand limits of g(x) are not equal as x→0.}]},