Page 06 MARKS 11. Given 3 2 1 x y x + = , use logarithmic differentiation to find dy dx . Write your answer in terms of x. 12. In the diagram below part of the graph of ( ) y f x = has been omitted. The point (−1, −2) lies on the graph and the line 1 3 2 y x = − is an asymptote. y 0 −3 (−1, −2) x Given that ( ) f x is an odd function: (a) Copy and complete the diagram, including any asymptotes and any points you know to be on the graph. (b) ( ) ( ) g x f x = . On a separate diagram, sketch ( ) g x . Include known asymptotes and points. (c) State the range of values of ( ) f x ′ given that ( ) 0 2 f ′ = . 13. Let n be an integer. Using proof by contrapositive, show that if 2 n is even, then n is even. 5 2 2 1 4