Question

Calculate the average rate of change for the function f(x) = x4 + 3x3 − 5x2 + 2x − 2, from x = −1 to x = 1

Answer 1

Average rate of change over the interval [a,b] for y=f(x) is given by f(b)−f(a)b−a Hence, average rate of change of from x=−2 to x=6 i.e. over the interval [−2,6] for y=f(x)=12x2 is given rate of change=f(6)−f(−2)6−(−2) As f(−2)=12(−2)2=2 and f(6)=12(6)2= rate of change=18−28=162=2