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bekas [8.4K]
3 years ago
10

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

Mathematics
1 answer:
stira [4]3 years ago
4 0
<h2>Answer:</h2>

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

<h2>Step-by-step explanation:</h2>

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 <em>what is the average rate of change of a function? </em>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

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