Engineering Mathematics, Volume I, Second Edition

2

Successive Differentiation, Mean Value Theorems and Expansion of Functions

2.1 SUCCESSIVE DIFFERENTIATION

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