u 3 mu... (7) (:5 transits)k Thejvolume of a right circular cylinder of radius r and height h, is V = 1rr2h. At a certain instant of time, the radius and height of the cylinder are 5 cm and 20 Cm, and the volume and the height are increasing at the rate of 500's cm3/ sec and 4 cm/sec, respectively. How fast is the radius of the cylinder increasing? (8) Use the following function f (s) = :sc'l/m for answering questions (a) - (f). (a) (2 marks) Find intervals where the function f (:s) is increasing and where it is decreas- ing. (b) (I mark) Find all critical numbers of f (1'). (c) (2 marks) Find all local maxima and minima of f (:r) and calculate the values of f (3:) at these points. ((1) (I mark) Find all inection points of f (3:). (e) (2 marks) Find the intervals where f (3:) is concave upward and where it is concave downward. (f) (3 marks) Sketch the graph of the function f (:s)