average rate of change equation with respect to x on interval [a,b]
delta f/delta x = f(b)-f(a)/b-a
The average rate of change of a function f(x) with respect to x on the interval [a,b] is given by the formula:
AROC = (f(b) – f(a)) / (b – a)
where f(b) represents the value of the function at the endpoint b, f(a) represents the value of the function at endpoint a, and (b – a) represents the change in the independent variable x from a to b.
Geometrically, the average rate of change is the slope of the secant line connecting the points (a, f(a)) and (b, f(b)) on the graph of the function.
This formula is used to find the average rate of change of a function over an interval, which provides information about how much the function changes on average per unit of interval length. This can be useful in applications such as physics, economics, and engineering where the rate of change of a variable is important to model and analyze.
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