In single-variable calculus, the difference quotient is usually the name for the expression {\frac {f-f(x)}{h}} which when taken to the limit as h approaches 0 gives the derivative of the function f.

What does find the difference quotient mean?

The difference quotient is a measure of the average rate of change of the function over an interval (in this case, an interval of length h). The limit of the difference quotient (i.e., the derivative) is thus the instantaneous rate of change.

What is a difference quotient at a point?

That is, the instantaneous rate of change at a given point. In order to measure this value, we use what is called a tangent line, and measure its slope to given the best possible linear approximation at a single point. ... The difference quotient allows us to compute the slope of secant lines.