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left and right derivative


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For the real function f, if

exists, this limit is the left derivative of f at a. Similarly, if

exists, this limit is the right derivative of f at a. (See limit from the left and right.) The derivative f΄(a) exists if and only if the left derivative and the right derivative of f at a exist and are equal. An example where the left and right derivatives both exist but are not equal is provided by the function f, where f(x)=| x | for all x. At 0, the left derivative equals −1 and the right derivative equals+1.

Subjects: Mathematics.


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