# What is the difference between the slope of a tangent and instantaneous rate of change of #f(x)#?

##### 1 Answer

There is no difference in the mathematical expressions for these things. The difference is interpretation (and setting).

The slope of a tangent line is a geometrical idea. It is tied to curves in a coordinate plane.

The instantaneous rate of change is a relationship between two variable quantities, one depending on the other.

The calculations or the algebra, if you like, are the same for both.

**Consider: #(f(x+h)-f(x))/h#. What is it?**

In terms of the symbols we write mathematically, there is no difference between the slope of a secant line, (geometry) the average rate of change (related variable quantities) and the difference quotient (an algebraic expression). But the mathematics has different meanings in different settings.

In a similar way (in the same way?):