This problem concerns a function about which the following information isknown:fis a differentiable function defined at every real number axf(0)=-12y=f'(x) has its graph given at center in Figure 3.1.16Figure 3.1.16.At center, a graph ofy=f'(x); at left, axes for plottingy=f(x); at right, axes for plotting y=f''(x).a. Construct a first derivative sign chart for f. Clearly identify all criticalnumbers off, where fis increasing and decreasing, and where f has localextrema.b.On the right-hand axes, sketch an approximate graph ofy=f''(x).c. Construct a second derivative sign chart for f. Clearly identify where fisconcave up and concave down, as well as all inflection points.d.On the left-hand axes, sketch a possible graph ofy=f(x).