f(x) = (105x³ − 128x² + 49x − 6) cos 2x, where x is in radians. The diagram shows a sketch of y = f(x).

a. Calculate f(0.2) and f(0.8).

b. Use your answer to part a to make a conclusion about the number of roots of f(x) in the interval 0.2 < x < 0.8.

c. Further calculate f(0.3), f(0.4), f(0.5), f(0.6) and f(0.7).

d. Use your answers to parts a and c to make an improved conclusion about the number of roots of f(x) in the interval 0.2 < x < 0.8.

YA 0.5- 0 -0.5 I r 1 = f(1)