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) --- 6 WORK AREA LINES (style=lined) --- 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`