4. This problem concerns a function about which the following information is known: f is a differentiable function defined at every real number a f(0) = -1/2 y= f'(x) has its graph given at center in Figure 3.1.17 2 Figure 3.1.17. At center, a graph of y = f'(x); at left, axes for plotting y = f(x); at right, axes for plotting y = f"(x). a. Construct a first derivative sign chart for f. Clearly identify all critical numbers of f, where f is increasing and decreasing, and where f has local extrema. b. On the right-hand axes, sketch an approximate graph of y = f"(x). c. Construct a second derivative sign chart for f. Clearly identify where f is concave up and concave down, as well as all inflection points. d. On the left-hand axes, sketch a possible graph of y = f(x).