question about rates

Question

what is one example of a rate that is decreasing?

also one that is increasing?

Answer 1

In the world of calculous, rate is the derivative. The derivative of position is velocity, and the derivative of velocity is acceleration. When one says "the derivative of x", you can think of that as "the rate of change for x". A derivative as we solve it, where the derivative of say x² is 2x, we know at point x=1, the instantaneous rate of change is 2.

The rate of the rate is the derivative of the derivative. A decreasing rate is negative, an increasing one is positive. So an increasing rate would be a positive second derivative, and a decreasing rate would be a negative second derivative.

Before calculous, you found the rate over a set bound with rise/run. Now you can find the rate at a point with a derivative.