Average Rate Of Change Formula For Steepness Of Math Functions

Average Rate of Change of f(x) on [a,b]

f'(x) = Positive

The average rate of change of a function f(x) on [a,b] is the ratio of the change in the value of the function over the change in the input variable, or:

Average Rate of Change of f(x) on [a,b] = (f(b) – f(a)) / (b – a)

This formula can be interpreted as the slope of the line connecting the two points (a, f(a)) and (b, f(b)) on the graph of the function f(x). Geometrically, this represents the average steepness of the function over the interval [a,b].

For example, if we want to find the average rate of change of the function f(x) = x^2 on the interval [1,3], we would use the formula:

Average Rate of Change of f(x) on [1,3] = (f(3) – f(1)) / (3 – 1)
= (9 – 1) / 2
= 4

So the average rate of change of f(x) on [1,3] is 4, which means that on average, the function increases by 4 units for every 1 unit increase in x over the interval [1,3].

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