Find the average rate of change of f from pi to 11pi/3. f (x) = cos (x/2) ... ?

The average rate of f is

[f (x2) - f (x1) ] / (x2 - x1)

x1 = pi, and x2 = 11pi/3

f (x2) = f (11pi/3) = cos [11pi/6) ]

f (x1) = f (pi) = cos [pi/2) ]=0

so M = f (x2) - f (x1) / 11pi/3 - pi = cos [11pi/6) ] / 8pi/3

finally M = 3cos [11pi/6) ] / 8pi