Describe how to determine the average rate of change between x = 2 and x = 4 for the function f(x) = 2x^3 + 1. Include the average rate of change in your answer.

Question

Describe how to determine the average rate of change between x = 2 and x = 4 for the function f(x) = 2x^3 + 1. Include the average rate of change in your answer.

Answer 1

56= average rate of change = slope of secant line

secant line is the line connecting points (2, f(2) ) and (4, f(4) ) = (2,17) and (4,129)

slope = (129-17)/(4-2) = 112/2 = 56

f(4) = 2(4^3 +1 = 2(64) + 1 = 129

f(2) = 2(2^3) +1 = 17