Average Rate of Change of f(x) on [a,b]
The average rate of change of a function f(x) on the interval [a, b] can be calculated by finding the slope of the line connecting the two points (a, f(a)) and (b, f(b))
The average rate of change of a function f(x) on the interval [a, b] can be calculated by finding the slope of the line connecting the two points (a, f(a)) and (b, f(b)).
To do this, we can use the formula for slope:
Average rate of change = (f(b) – f(a)) / (b – a)
Here’s how you can calculate the average rate of change step by step:
1. Start by finding the y-values of the function at points a and b. Evaluate f(a) and f(b) by substituting the respective x-values into the function.
2. Calculate the difference in the y-values: f(b) – f(a).
3. Find the difference in the x-values: b – a.
4. Divide the difference in y-values by the difference in x-values: (f(b) – f(a)) / (b – a).
The resulting value will give you the average rate of change of the function f(x) on the interval [a, b]. This value represents how the function’s output changes, on average, for every one-unit change in the input over the interval [a, b].
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