MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
A function h is defined by
h(x)=x−2x2−4.
The graph of h has a removable discontinuity at x=2.
(a) Determine the domain of h and express your answer in interval notation.
(b) Explain whether h is differentiable at x=2. Include a discussion of the relationship between differentiability and continuity at that point.
(c) A new function k is defined by k(x)=h(x) for x=2 and k(2)=4. Determine whether k is differentiable at x=2. Justify your conclusion.