Question

Can average rate of change be negative?

Solution
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Yes.Remember that the rate of change could be things like acceleration, not just speed.Even through 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.grapgh $$\left\{\sin x [-10,10,-5,5]\right\}$$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.

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