Given f(x)= 9-x2 Q(x) _P(x) _ R(x) find each of the following: (24 pts) (a) The equations of any Vertical Asymptotes by finding the zeros of Q(x)....

5. Given f(x)=9-x2 Q(x)_P(x) _ R(x) find each of the following:(24 pts)(a) The equations of any Vertical Asymptotes by finding the zeros of Q(x).(b) The equations of any Horizontal Asymptotes. Use: ( lim f (x) = L=> y = L is a horizontal asymptote).(c) The critical numbers of f (x) and make a sign analysis (or sign line or table) of f'(x).(d) The open intervals on which f (x) is increasing or decreasing.(e) Make a sign analysis (or sign line or table) of f"(x) and find the open intervals on which f (x) is concaveupward or concave downward.(f) Any local extreme values.(g) Sketch the graph and label the coordinates where there are local extreme values.Also label the inflection points and show the equations of any asymptotes.