Calculus, MET1 2016 VCAA 6a Let `f : [– pi, pi] → R`, where `f (x) = 2 sin (2x) - 1`. Calculate the average rate of change of `f` between `x = −pi/3` and `x = pi/6`. (2 marks) Show Answers Only `(4sqrt3)/pi` Show Worked Solution `text(Average rate of change)` `= (f(pi/6) – f(−pi/3))/(pi/6 – (−pi/3))` `= [(2sin(pi/3) – 1) – (2sin(−(2pi)/3) – 1)] xx 2/pi` `= [(2 xx (sqrt3)/2 – 1) – (2 xx (−sqrt3)/2 – 1)] xx 2/pi`♦ Mean mark 48%. MARKER’S COMMENT: Evaluating `f(-pi/3)` caused significant problems here. `= (sqrt3 – 1 + sqrt3 + 1) xx 2/pi` `= (4sqrt3)/pi`