Question

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

Answer 1

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

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=(f(x_(2))-f(x_(1)))/(x_(2)-x_(1)) \\ \\ ARC=(17-5-(17-1))/(5-1) \\ \\ ARC=-1`