3t3 3t2(t2- 9} , 1&W+m r _ _ t2 _ 3 With 9 (t) (t2 _ 3)2 (:2 3r! ' 1. Let g(t) = and g\"(t) = (a) Determine the domain of g. (b) Determine the intervals of increase and decrease. (c) Determine the intervals of concave up and concave down. (d) Use your work above to answer the following: I The graph of g is concave up and increasing on the interval I The graph of g is concave up and decreasing on the interval I The graph of g is concave down and increasing on the interval I The graph of g is concave down and decreasing on the interval I The graph of g has inection point(s) at 2. Sketch the graph of a function f such that (a) to (k) below hold. For full marks clearly and carefully label all intercepts, relative extrema, inflection points, and asymptotes. (a) Domain: (-00, co). (b) Continuous for all real numbers. (c) Differentiable everywhere except at x = -3. (d) f(0) = 6. (e) lim f(x) = 0. 20 -+ 00 ( f ) f' ( - 2 ) = f'(0) = 0. (g) f'(x) 0 on (-2, -1) and (2, 00). (k) f"(2)