MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions
Problem
Let f′(x)=∣x−1∣ for all real x, and suppose f is twice differentiable wherever possible. Which of the following statements about f′′ is correct?
(a) f′′(x)=0 for x=1, and f′′(1) does not exist
(b) f′′(x) does not exist for any real x
(c) f′′(x)=−1 for x<1, f′′(x)=1 for x>1, and f′′(1) does not exist
(d) f′′(x)=1 for x<1, f′′(x)=−1 for x>1, and f′′(1) does not exist