Question

Given f(x) = 17-xwhat is the average rate of change in f(x) over the interval [1, 5]?

Answer 1

Answer:

The average rate of change in f(x) over the interval [1, 5] is -1

Step-by-step explanation:

Hi! Let me help you to understand this problem. Here we have the following function:

$f(x) = 17-x$

We need to compute the Average Rate of Change (ARC) in $f(x)$ over the interval $[1, 5]$. So what is the average rate of change of a function? In general, for a nonlinear graph whose slope changes at each point, the average rate of change between any two points $(x_{1},f(x_{1}) \ and \ (x_{2},f(x_{2})$ is defined as the slope of that line through that two points. Here we have a linear function, so the average rate of change will be the slope of the line:

So:

$ARC=m=-1$

This can also be calculated as:

$ARC=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}} \\ \\ ARC=\frac{17-5-(17-1)}{5-1} \\ \\ ARC=-1$