Limit Definition of the Derivative
We learned in algebra that the slope of a line can be represented by a constant, “m”. However, when we attempt to find the slope of a curve we notice the slope changes depending on x. This new function of x that determines the slope of f(x) at any point is called the derivative of f(x). It turns out that we can use limits to find this derivative function. *These can be long and tedious, but hang in there – soon you will learn a shortcut for how to take a derivative.