The graph of f is shown. Graph f, f' and f'' on the same set of coordinate axes.
E)none of the above

Question

The graph of f is shown. Graph f, f' and f'' on the same set of coordinate axes. 
E)none of the above

Quizplus · Accepted Answer

- To graph f', we need to find the derivative of f. We can see from the graph that f is decreasing on the interval (-∞,-1) and (1,∞), and increasing on the interval (-1,1). Therefore, f' is negative on (-∞,-1) and (1,∞), and positive on (-1,1). Furthermore, f has two local maximum points and one local minimum point, which means that f' has two roots and one vertical asymptote. One possible graph for f' is shown in blue in choice C.
- To graph f'', we need to find the derivative of f' and plot it on the same set of axes. We can see from the graph of f' that it has a root at x=0 and a vertical asymptote at x=1. Therefore, f'' has a vertical asymptote at x=1 and a delta function (or point discontinuity) at x=0. Furthermore, f' is positive on (-1,0) and (0,1), and negative on (-∞,-1) and (1,∞), which implies that f'' is decreasing on (-∞,-1) and (1,∞), and increasing on (-1,0) and (0,1). One possible graph for f'' is shown in green in choice C.

The Graph of F Is Shown