The more I think about it, rate of change is a tricky concept. When you're moving at 60 mph, your position is changing but the rate at which it is changing is constant. A body falling in a vacuum, say 1,000 miles away from earth, is changing speed, accelerating at a steady rate.

Best I can recall, calculus has two main functions: to find the slope of any line tangent to an X - Y axis graph at any point on it -- the derivative; and to find the area between a non - linear graph and, say, the X axis -- the integral.

Imagine a graph of the function Y = sinX + 2. Since the sin of any angle will always be between one and negative one, this function will be a sin wave completely above the X axis. With calculus, ideally you could find the area between the graph and the X axis for some portion of the graph. I say ideally because I can't recall if it only works with polynomials, where you have a finite number of constants and variables which are combined using only addition, subtraction, multiplication, and non-negative whole number exponents (raising to a power). This from Wikipedia, better than I could have said it. The sin function is not one of those. Not sure how you could use the ability to find the area between a curved line and the X axis, or between two curved lines, dlineated by straight lines on either end. I understand it opens all sorts of boxes though.

More to the point, derivatives find the slope of a line tangent to the graph at any point on the graph and give a value for the rate of change of that graph at that point. Again from Wikipedia: A derivative is an instantaneous rate of change: it is calculated at a specific instant rather than as an average over time.

And again, I'm not sure exactly what that operation is used for but I imagine physicists and aerospace engineers know quite well.

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