Question

The graph of f(x) = 2x + 1 is shown below. Explain how to find the average rate of change between x = 0 and x = 3. Graph of 2 to the power of x plus 1

Answer 1

The general formula for "average rate of change of f(x) over the interval [a,b] is

f(b) - f(a)
ave r of c = -----------------
b - a

In this problem, f(x) = 2x + 1, f(b) = 2(3) = 7 and f(0) = 2(0) + 1 = 1.

Then the average r. of c. of f(x) = 2x + 1 over [0,3] is:

7 - 1
------------ = 6/3 = 2 (answer) Note that 2 is the slope of this straight line!
3 - 0