Average Rate of Change of f(x) on [a,b]
y-y1=m(x-x1)
The average rate of change of a function f(x) over an interval [a, b] is equal to the quotient of the change in the function over the interval, and the length of the interval. It measures the average slope of the function over the interval [a, b].
The formula for the average rate of change is:
average rate of change = (f(b) – f(a)) / (b – a)
where f(a) and f(b) represent the values of the function at the endpoints of the interval [a, b].
For example, if f(x) = x^2 and we want to find the average rate of change of f(x) on the interval [2, 4], we can use the formula:
average rate of change = (f(4) – f(2)) / (4 – 2)
= ((4)^2 – (2)^2) / 2
= (16 – 4) / 2
= 6
Therefore, the average rate of change of f(x) on the interval [2, 4] is 6. This means that on average, the function f(x) increases by 6 units for every 1 unit increase in x over the interval [2, 4].
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