Find f'(x).

Find using your answer to part (a) the x-coordinate of

(i) the local maximum point;

(ii) the local minimum point.

15x² – 8x + 1     (A1)(A1)(A1)     (C3)

Note: Award (A1) for each correct term.

[3 marks]

15x² – 8x +1 = 0     (A1)(ft)

Note: Award (A1)(ft) for setting their derivative to zero.

(i) \((x =)\frac{1}{5}(0.2)\)     (A1)(ft)

(ii) \((x =)\frac{1}{3}(0.333)\)     (A1)(ft)     (C3)

Notes: Follow through from their answer to part (a).

[3 marks]

Many candidates lost 1 mark in part (a) through not realizing that the derivative of x is 1. As a consequence,  15x² – 8x proved to be a popular answer.

Very few candidates gained the marks in part (b) to find the maximum and minimum point. Although the question indicated to use their answer to part (a), very few candidates set the derivative to zero which would have given them 1 mark. It seemed as if many candidates were trying to use their calculators to find the coordinates but could not find which was the maximum and which was the minimum.