Determining the unknown constant LetDetermine a value of a (if possible) for which f′ is c...

Determining the unknown constant Let

Determine a value of a (if possible) for which f′ is continuous at x = 1.

64-67. Approximating derivatives Assuming the limit exists, the definition of the derivative  implies that if h is small, then an approximation to f′(a) is given by

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If h > 0, then this approximation is called a forward difference quotient; If h < 0, it is a backward difference quotient. As shown in the following exercises, these formulas are used to approximate f at a point when f is a complicated function or when f is represented by a set of data points.