Successive Differentiation, Mean Value Theorems and Expansion of Functions


Let f be a real-valued function defined on an interval [a, b]. Then, it is said to be derivable at an interior point c if images exists. This limit, if exists, is called the derivative or the differential coefficient of the function at x = c and is denoted by f ′(c).


The above limit exists, if both the following limits exist and are equal:

  1. images called the left-hand derivative and denoted by f ′(c – 1),
  2. called the right-hand derivative and denoted ...

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