Suppose that the following information is known about a function f the graph of its derivative, y f'(z), is given in Figure 5 1 1 Further, assume that f' is piecewise linear (as pictured) and that for a 0 and z2 6, f'(z) 0 Finally, it is given that f(0) 1 MI y f'(x) 3 3 5 1t 1t 3 3 Figure 5 1 1 At left, the graph of y f'(x) at right, axes for plotting y f(r) a On what interval(s) is f an increasing function On what intervals is f decreasing b On what interval(s) is f concave up concave down c At what point(s) does f have a relative minimum a relative maximum d Recall that the Total Change Theorem tells us that f(1) f(0) f'(2) dz 3D What is the exact value of f(1) e Use the given information and similar reasoning to that in (d) to determine the exact value of f(2) f(3), f(4) f(5) and f(6) f Based on your responses to all of the preceding questions, sketch a complete and accurate graph of y f(x) on the axes provided, being sure to indicate the behavior of f for a 0 and a 6

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Suppose that the following information is known about a function f: the graph of its derivative, y = f'(z), is given in Figure 5.1.1.

Suppose that the following information is known about a function f: the graph of its derivative, y = f'(z), is given in Figure 5.1.1. Further, assume that f' is piecewise linear (as pictured) and that for a

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