2x2 - 7x+8 12. For the rational function g(x) x-2 . . a) Find its critical points.b) Find its vertical asymptote and determine the behaviour of g (x ) on either side of the VA. c) Find its oblique asymptote and determine the behaviour of g (x) either above or below the OA as x -> too and x-> co.y - axis 10 -9 -8 -7 6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 x - asis d) Use this information to sketch a graph of 8(x) .13. Differentiate the following. Simplify your derivatives by common factoring. 3) f 00423612") b) y=etm2x c) g (x) = x2 cos3x2 5x sin 5x 14. The population P of a bacterial culture, being treated by a drug to kill them off, is described by L L the lnction P(t)=60e3 e2, where t is in minutes. When does the population reach a maximum, and what is this maximum value? [4]