A function is represented by two straight-line segments that meet at the point
MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
A function f is represented by two straight-line segments that meet at the point (3,5). One segment has slope 2 for x<3, and the other has slope −1 for x>3. Which statement best describes f′(3)?
(a) f′(3)=2 because the slope of the segment to the left of x=3 is 2
(b) f′(3) is undefined because the slopes from the left and right are different
(c) f′(3)=21 because the derivative at the corner should be the average of the two slopes
(d) f′(3)=−1 because the slope of the segment to the right of x=3 is −1