The difference quotient is essential in the definition of the derivative of a function.
the slope of the secant line is an average rate of change
The derivative is used to find the slope of the tangent line to the graph of a function at a point.
the slope of the tangent line is an instantaneous rate of change
The derivative is found by letting h approach zero in the difference quotient.
i.e. the slope of the secant line approaches the slope of the tangent line as h gets close to zero