Question

Can the instantaneous rate of change be zero?

Answer 1

Yes, if you consider:
A constant function.
For example: the function `f(x)=5` is a constant and so never changes, giving you a rate of change (average or instantaneous) equal to zero.
If you consider a car moving on a straight line at constant velocity, say 30 km/h, it will have an instantaneous rate of change of velocity (known as acceleration) equal to zero.

You can also have a changing function (as a quadratic) that at certain points has zero instantaneous rate of change. These are points where your function changes inclination or slope. We call them points of maximum or minimum. At these points your function is neither going up nor down....!!!