Question

Hello! I am stuck on this one question and would really like some help either solving or a good explanation on how to solve would be sufficient. Thanks!
Question: Explain how to find the average rate of change for f(x) from x = 4 to x = 7.

Answer 1

Average rate of change is given by: \[
\frac{f(x_f)-f(x_i)}{x_f-x_i}
\]In this case, \(x_i=4\) and \(x_f=7\), so we have:\[
\frac{f(7)-f(4)}{7-4} = \frac{f(7)-f(4)}{3}
\]

Answer 2

the rate of change can be compared to finding the slope of a line .
f(x) considered y, means the function of x in that as x changes then y changes
when x is 4 y is the value for f(4)
when x = 7 y is the value for f(7)
the change is from the difference in the y values over the period of the change in the x values
this is shown in the formula above