Closes Points vs x-values in Definition 3.1.7 #598 #608
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I agree that saying x-values makes more sense than a point. However, I'm not sure I like our definition here. I think it would make more sense to define the average rate of change on a given interval and point out that it's the end points of the interval that we are using as our two points. As is, it kind of feels like we are saying that to find the average rate of change of a function we just pick two x-values a and b. But average rate of change depends on an interval. I'm also not sure that a description of how to plug in to the formula belongs in its definition. Maybe a remark? "Notice we are using both the |
| An <term>average rate of change</term> of a function calculates the amount of change in one item divided by the corresponding amount of change in another. | ||
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| An <term>average rate of change</term> of a function calculates the amount of change in one item divided by the corresponding amount of change in another. | |
| </p> | |
| The <term>average rate of change</term> of a function on a given interval measures how much the function's value changes per unit on that interval. For a function <m>f(x)</m> on the interval <m>[a,b]</m>, it is calculated by the following expression: | |
| <me>\dfrac{f(b)-f(a)}{b-a}. </me> | |
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| @@ -174,7 +174,7 @@ | |||
| An <term>average rate of change</term> of a function calculates the amount of change in one item divided by the corresponding amount of change in another. | |||
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| <p> | |||
| To calculate the average rate of change for any function <m>f(x)</m>, we pick two points, <m>a</m> and <m>b</m>, and evaluate the function at those two points. We then find the difference between the <m>y</m>-values and <m>x</m>-values to calculate the average rate of change: | |||
| To calculate the average rate of change for any function <m>f(x)</m>, we pick two <m>x</m>-values, <m>a</m> and <m>b</m>, and evaluate the function at those two <m>x</m>-values. We then find the difference between the <m>y</m>-values and <m>x</m>-values to calculate the average rate of change: | |||
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Then this part could be a remark instead of a definition? Something like:
Remark: Notice that to calculate the aroc over an interval [a,b], we are using the two endpoints of the interval, namely (a,f(a)) and (b,f(b)).
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And then delete the expression for the formula below.
Closes #598