Average rate of change

Average rate of change

Postby Guest » Sat Feb 02, 2019 7:09 pm

Consider the function f(x)=3x-4.
Find the average rate of change between the points (a,f(a)) and (b,f(b))

Re: Average rate of change

Postby HallsofIvy » Wed Mar 06, 2019 11:32 am

Oh, come on! Do you really have no idea how to calculate an "average rate of change"? That doesn't even require "Calculus" since Calculus introduces the instantaneous rate of change. The function give is f(x)= 3x- 4 so that f(a)= 3a- 4 and f(b)= 3b- 4. The "change" as x goes from a to b is f(b)- f(a)= 3b- 4- (3a- 4)= 3b- 3a= 3(b- a). Since that was over a period b- a, the rate of change is 3(b- a)/(b- a)= 3. This function is "linear" and linear functions have constant rate of change.

I presume this is in the first couple of weeks of a Calculus class. It is going to get harder! And you learn by doing, not by watching some one else do it! You are welcome to post questions here but in future please try to do the problem yourself first and, if you are not able to solve it, post what you tried here so we will know what hints will help you do the problem your self.

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