Difference quotient
The difference quotient can be used to find the slope of a curve, as well as the slope of a straight line. After we find the difference quotient of a function and take the limit as two points get closer and closer to each other, we have a new function, called the derivative. To find the slope of the curve or line, we input the value of x to get the slope. The process of finding the derivative via the difference quotient is called differentiation.