The simplest examples of functions, hence the best place to start our investigation, are constant functions. Recall that derivatives measure the rate of change of a function at a given point. This means the derivative of a constant function is zero. Here are some ways to think about this situation. {{CMD_14}} {{CMD_15}} The constant function plots a horizontal line---so the slope of the tangent line is {{MATH_16}}. {{CMD_17}} If {{MATH_18}} represents the position of an object with respect to time and {{MATH_19}} is constant, then the object is not moving, so its velocity is zero. Hence {{MATH_20}}. {{CMD_21}} If {{MATH_22}} represents the velocity of an object with respect to time and {{MATH_23}} is constant, then the object's acceleration is zero. Hence {{MATH_24}}. {{CMD_25}} The examples above lead us to our next theorem. To gain intuition, you should compute the derivative of {{MATH_26}} using the limit definition of the derivative.