Question

Can average rate of change be negative?

Answer 1

Yes.

Explanation:

Remember that the rate of change could be things like acceleration, not just speed.

Even though speed itself is a scalar and cannot be negative, you can have a negative velocity by adding direction (which makes it a vector)

Also, if your speed is decreasing, you decelerate, which is another word for negative acceleration.

For example, let's say you had the function `sin(x)` to show the speed in respect to time.

graph{sinx [-10, 10, -5, 5]}

We can see that your speed increases until it reaches a certain point. There, we see that it decreases to a certain point. The decrease represents negative rate of change. (Deceleration in this case.)