We consider the derivative from an analytic point of view; digging into the algebraic notation and manipulation for instantaneous rates of change.
One of the major uses of derivatives is to determine where functions are increasing and decreasing. In this video we will see how derivatives accomplish this, and discuss why this might be useful.
We have seen how derivatives can tell us if a function is increasing or decreasing, and even more importantly, it gives us an objective metric to determine how quickly the function is increasing or decreasing. This can be useful in a number of ways, from getting a specific value for something like your speed, to being able to contrast the rate of change of two functions to determine which one is growing faster or slower. Indeed, this will allow us to even build a hierarchy of growth rates for functions. This idea of increasing or decreasing will come up over and over and over again as we progress through various applications of derivatives.
