Question

What is the average rate of change of the function over the interval x = 0 to x = 6?

Answer 1

The average rate of change is given by:
[f(b)-f(a)]/[b-a]
Given that:
f(x)=(2x-1)/(3x+5)
thus
ARC=[f(6)-f(0)]/[6-0]
f(6)=(2*6-1)/(3*6+5)=(12-1)/(18+5)=11/23
f(0)=(2*0-1)/(3*0+5)=(0-1)/(0+5)=-1/5
thus
ARC=(11/23-(-1/5))/(6-0)=(11/23+1/5)/6=(78/115)/6=13/115