I got this investigation to do for homework today. The question is below:

The regression equation represents the derivative function. Compare the original equation and the derivative equation. What relationship do you notice?

Comparing f(x) to f’(x), f’(x) represents the instantaneous rate of change of f(x). The pattern to determine the instantaneous rate of change without graphing technology is to multiply the coefficients of each term by the power of the term, then reduce the exponent by 1.

Is that a good enough answer? Or is there a proper mathematical terminology for this pattern?

Also, what is the derivative of a constant function. For example, y = 3. I believe it is 0 however my math is saying it is undefined.