Average Rate of Change
Slope of secant line between two points, use to estimate instantanous rate of change at a point.
The average rate of change is a concept used in mathematics to determine the rate at which a function changes over a specific interval or range of values. It is found by calculating the difference between the function values at two points divided by the difference in their corresponding input values.
For example, if we have a function f(x) = x^2 and we want to find the average rate of change between x=2 and x=5, we would use the formula:
average rate of change = (f(5) – f(2)) / (5 – 2)
= [(5^2) – (2^2)] / 3
= (25 – 4) / 3
= 7
So, the average rate of change of the function f(x) = x^2 between x=2 and x=5 is 7.
The average rate of change can be used to describe the slope of a function, which is the rate at which it changes at a given point. In calculus, it is also used to find the instantaneous rate of change of a function using the limit concept.
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