Let A = {1, 2, 3, 4}. Determine whether relation is reflexive, irreflexive, symmetric, asymmetric, antisymmetric or transitive : R1 = {(1, 2), (1, 3), (3, 1), (1, 1), (3, 3), (3, 2), (1, 4), (4, 2), (3, 4)}
R2 = {(1, 3), (4, 2), (2, 4), (3, 1), (2, 2)}.

The average number of vehicles waiting in line to enter a parking lot can be modeled by the function f left parenthesis x right x squared over 2 left parenthesis 1 minus x right parenthesis endfraction , where x is a number between 0 and 1 known as the traffic intensity. find the rate of change of the number of vehicles waiting with respect to the traffic intensity for the intensities (a) xequals0.3 and (b) xequals0.6.