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It can be positive or negative, or even both - at different stages.For example, the rate of change of the balance in my bank account is positive at the end of the month - when my pay goes in - but it is negative for most of the rest of the time while I am spending it!
if a number can change randomly it is called a variable
For continuous functions, yes.
0. There is no x in your equation so regardless of how you change your input, the output y never changes.
The first derivative is the rate of change, and the second derivative is the rate of change of the rate of change.