Rate of change vs. average rate of change of a functionWhat is the difference between...

Kenya Leonard

Kenya Leonard

Answered

2022-07-16

Rate of change vs. average rate of change of a function
What is the difference between the both? I am trying to find a separate definitions for both in a textbook, but it only defines average rate of change.
I know that average rate of change is:
c h a n g e i n y c h a n g e i n x
But what is just rate of change then?

Answer & Explanation

Kendrick Jacobs

Kendrick Jacobs

Expert

2022-07-17Added 16 answers

The average rate of change is defined over some finite interval Δ x to be
Δ y Δ x
The rate of change is the rate at which the function changes at one particular point and is found by taking the limit
lim Δ x 0 Δ y Δ x
Note that in the case of a linear function, y=mx+c, the rate of change and the average rate of change are identical (they both equal m).

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