Question

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

Answer 1

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