# Details are in the PD fileQuestion 1(a) A function is defined by the expression?

Details are in the PD fileQuestion 1(a) A function is defined by the expression?(?) ＝ ??3 − ?? − ?(i) Choose values for a, b and c, such that a, b and c ∈ ℕ and ?, ? ??? ? ≠ 0. Enter these values into ?(?) and draw a graph of the relation using Excel or on graph paper.[15 Marks](ii) Find the turning point(s) of your graph.[5 Marks](iii) The function ?(?) is a line that passes through these turning points. Find the equation of ?(?).[10 Marks](iv) Draw ?(?)on the graph you drew in (i). [5 Marks](b) Provide an example to illustrate each of the following differentiation rules(i) the product rule(ii) the quotient rule and(iii) the chain rule[15 Marks](c) The height above level ground of a portion of a rollercoaster track is modelled by the function?(?) ＝ 2?3 3?2(i) Find ?′(?), i.e., the derivative of ?(?). [5 Marks](ii) Find ?′′(?)[5 Marks](iii) Use this derivative to find the maximum height above the track at this point on