What is the actual definition of Left Hand Derivative?
I bumped into this site and the second white box on their site gives the definition. Is that wrong?
What is the correct one then?
1 Answer
$\begingroup$The left-hand and right-hand derivatives of $f$ at $a$ are defined by $$ f'_{-}(a)=\lim_{h\to 0^-}\frac{f(a+h)-f(a)}{h} $$ and $$ f'_{+}(a)=\lim_{h\to 0^+}\frac{f(a+h)-f(a)}{h} $$ if these limits exist. Then $f'(a)$ exists if and only if these one-sided derivatives exist and are equal.
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