Abstract
One of the most important properties of a continuous function is the intermediate value property. Even though derivatives are not always continuous, they do always possess the intermediate value property. The derivatives are sometimes described as being “Darboux continuous,” not because they are always continuous, but because they always possess the intermediate value property characteristic of continuous functions. It is not always possible to obtain higher order derivatives. Derivatives are used to calculate the value of indeterminate forms. The method used for this is known as L’Hopital's rule.
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