The piecewise-defined function has a graph consisting of two line segments: h(x)=…
MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
The piecewise-defined function h has a graph consisting of two line segments:
h(x)={−2x+6,x−3,0≤x<3,3≤x≤5.
Which statement about the first derivative h′ is true?
(a) h′=−2 for 0<x<3, h′=0 at x=3, and h′=1 for 3<x<5.
(b) h′=−2 for 0<x<3, h′=1 at x=3, and h′=1 for 3<x<5.
(c) h′=−2 for 0<x<3, h′ is undefined at x=3, and h′=1 for 3<x<5.
(d) h′=−2 for 0<x<3, h′=−2 at x=3, and h′=1 for 3<x<5.