Wireless

Duration 90 Minutes Part 1: MULTIPLE CHOICE QUESTIONS You may solve all questions. Each question is worth 1.5 marks. Your grade in this part is that of the best 4 questions, giving a total of 6 possible marks. Q–1: The domain of the function f  x   a) b) c) d) e) R\{0} R\{0, −1} (0, ∞) (− ∞, 0) None of the above

1 is x x

3

Q–2: An equation of the line which is perpendicular to the line y +16x = 8 is a) x + 4y = 2 b) x − 4y = 2 c) x − 16y = 8 d) x + 16y = 8 e) None of the above Q–3: The largest open interval(s) over which f x   2 x 3  3x 2  12 x is increasing is a) (−1, 2) b) (−∞,−1) c) (2, ∞) d) (–∞, −1) and (2, ∞) e) None of the above Q–4: If g x   3 4 x  5 , then g′(1) = a) 5 b) 3 c) 2 d) 1 e) None of the above

Q–5: A local maximum of the function f x   5  12 x  x 3 occurs when x is a) –2 b) 2 c) 0 d) 5 e) None of the above

Part 2: ESSAY QUESTIONS

Each question is worth 8 marks. You should answer only THREE out of the four questions, giving a total of 24 possible marks.

x2 1 and g x   Q–1: [4×2 Marks] Let f x   2 . x 1 x 1 a) Find the domains of f (x) and g(x). b) Find f (g(x)) and describe its domain.   5   c) Find g  f    2  .    d) Find the vertical and horizontal asymptotes of the function f (x).

Q–2: [3+3+2 Marks]

1 . x 1 40 b) Find an equation of the tangent line to the graph of f  x   at 3x  7 the point whose x-coordinate is 3. c) Find the points on the graph of f x   x 4  4 x 3  20 at which the tangent line is horizontal.

a) Use the definition of the derivative to find f ′ (x) if f  x  

Q–3: [3+3+2 Marks] Let f x   2 x 3  3x 4  12 x  20, x   3, 3. a) Find the intervals on which the function f is increasing or decreasing and find the local maximum and minimum, if any. b) Find the intervals on which the graph of f is concave up or concave down and find the points of inflection, if any. c) Sketch the graph of f .

Q–4: [8 Marks] A box whose volume is 36 cm3 and its...