MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
Function g is defined by g(x)=∣x−3∣ for all real x.
Answer the following questions about g and its derivative.
(a) Determine the domain of g. Express your answer in interval notation.
(b) Explain why g fails to be differentiable at x=3. Your explanation should refer to the two one-sided limits of the difference quotient and compare their values.
(c) Identify the domain of g′. Justify your answer in words and with appropriate notation.