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in this lesson were going to focus on calculating the average rate of change of a function over an interval so heres the formula the average rate of change is f of b minus f of a over b minus a on the interval a to b so a and b are x values f of a and f b you could think of them as the y values so first lets calculate f of a and f b in this example a is one b is three so lets calculate f of one we just need to plug it into this equation so its going to be one squared plus four times one minus five so thats going to be one plus four minus five one plus four is five five minus five is zero so f of one is zero now what about f of three thats going to be three squared plus four times three minus five three squared three times three is nine four times three is twelve and 12 minus 5 is 7 so we have 9 plus 7 which is equal to 16. so thats f of 3. so now lets use this expression so thats going to be f of three minus f of one divided by three minus one f of three is sixteen f of one i