Given a function, it is often useful to know the rate at which the function changes. To give you a feeling why this is true, consider the following: {{CMD_7}} {{CMD_8}} If {{MATH_9}} represents the {{CMD_10}} of an object on a line (with respect to time), the rate of change gives the {{CMD_11}} of the object. {{CMD_12}} If {{MATH_13}} represents the {{CMD_14}} of an object with respect to time, the rate of change gives the {{CMD_15}} of the object. {{CMD_16}} If {{MATH_17}} represents the revenue generated by selling {{MATH_18}} objects, the rate of change gives us the {{CMD_19}}, meaning the additional revenue generated by selling one additional unit. Note, there is an implicit assumption that {{MATH_20}} is quite large compared to {{MATH_21}}. {{CMD_22}} If {{MATH_23}} represents the cost to produce {{MATH_24}} objects, the rate of change gives us the {{CMD_25}}, meaning the additional cost generated by selling one additional unit. Again, there is an implicit assumption that {{MATH_26}} is quite large compared to {{MATH_27}}. {{CMD_28}} The rate of change of a function can help us approximate a complicated function with a simple function. {{CMD_29}} The rate of change of a function can be used to help us solve equations that we would not be able to solve via other methods. {{CMD_30}}