April 14, 2013

## How to find the rate of change using f(x)= x2-1?

I don’t understand how to solve this problem to find the rate of change.
It says: find the rate of change when x1= -2 and x2= 6 I tried to solve it and got 6-1=-2 , but I don’t know what to put down for the rate of change. I have several problems like this and I would really appreciate if you could explain to me how to work it out step by step. Thank you for your help!
I still don’t understand how you got that answer.

You don’t need to use calculus to get this answer.

The rate of change is the “change in y” divided by the “change in x.” In your problem, they’re using ƒ(x) instead of y, but they mean the same thing. Also, your function is usually written ƒ(x) = x^2 – 1, where x^2 means x-squared.

You know that x1 = -2, so ƒ(x1) = (-2)^2 – 1 = 3; and x2 = 6, so ƒ(x2) = 6^2 – 1 = 35.

The change in y is ƒ(x2) – ƒ(x1) = 35 – 3 =32.

The change in x is x2 – x1 = 6 – (-2) = 8.

The rate of change is the change in y divided by the change in x, or 32 divided by 8, which equals +4. That’s your answer.

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