Suppose that the following information is known about a function f: the graph of its derivative,...

 

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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. 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. 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.