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

- f: The graph is shown. - f': The derivative of f is shown by the increasing/decreasing behavior of the graph of f. When the graph of f is increasing, f' is positive, when the graph of f is decreasing, f' is negative. The critical points (where f'=0) are marked on the graph. For example, the critical point at x=1 has f'>0 before it and f'<0 after it, indicating a local maximum. - f'': The second derivative of f is shown by the concavity of the graph of f. Where the graph of f is concave up, f'' is positive, where the graph of f is concave down, f'' is negative. The inflection points (where f''=0) are marked on the graph. For example, the inflection point at x=2 has f''>0 before it and f''<0 after it, indicating a change from concave up to concave down.

The Graph of F Is Shown