A function is defined on the interval and its graph has the following…
MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
A function g is defined on the interval [−2,4] and its graph has the following characteristics:
• For x<−1, the graph is smooth.
• At x=−1, a jump discontinuity occurs.
• For −1<x<2, the graph is smooth.
• At x=0, the graph has a cusp.
• At x=2, the graph is smooth but the tangent line is vertical.
• For 2<x<4, the graph is smooth.
• At x=4, the graph ends with a filled dot (no values for x>4).
At which set of x-values does g fail to be differentiable?
(a) {−1,0,2}
(b) {0,2,4}
(c) {−1,2,4}
(d) {−1,0,2,4}