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Define Differentiability of a Function at a Point. - Mathematics

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Question

Define differentiability of a function at a point.

 

Solution

Let  

\[f(x)\]  be a real valued function defined on an open interval 
\[(a, b)\]  and let  
\[c \in (a, b)\]
Then  
\[f(x)\]  is said to be differentiable or derivable at 
\[x = c\]
\[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\] exists finitely.
\[f'(c) = \lim_{x \to c} \frac{f(x) - f(c)}{x - c} .\]
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Chapter 10: Differentiability - Exercise 10.3 [Page 17]

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RD Sharma Mathematics [English] Class 12
Chapter 10 Differentiability
Exercise 10.3 | Q 1 | Page 17

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