The function is continuous on the interval and its graph consists of three line…
MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity
Problem
The function g is continuous on the interval 0≤x≤9 and its graph consists of three line segments that join the points (0,4), (3,1), (6,5), and (9,2) in that order.
Throughout this problem, let g′ denote the derivative of g.
(a) Sketch a carefully labeled graph of y=g′(x) for 0≤x≤9. Include all critical values of g′ on the x–axis and indicate the numerical value of g′ on each open interval where it is constant.
(b) Determine all x–values in 0≤x≤9 at which g′ is not continuous. For every discontinuity, classify it as removable, jump, or infinite and provide a brief justification based on your graph from part (a).