How do you find the average rate of change of f(x)=4xf(x)=4x over the interval [0, 9]?

1 Answer
mason m
May 19, 2017

44

Explanation:

The average rate of change of a function f(x)f(x) on the interval [a,b][a,b] is given by the slope of the seant line connecting (a,f(a))(a,f(a)) and (b(f,b))(b(f,b)), or:

(f(b)-f(a))/(b-a)f(b)−f(a)b−a

Here, where f(x)=4xf(x)=4x, we see that we have a linear function, where the rate of change is always 44, but we can still show that the average rate of change will be 44 using the formula:

=(4(9)-4(0))/(9-0)=(4(9-0))/(9-0)=4=4(9)−4(0)9−0=4(9−0)9−0=4

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