Left and right derivatives for JEE

Formula

\[f'_{-}(a)=\lim_{h\to 0^-}\frac{f(a+h)-f(a)}{h},\qquad f'_{+}(a)=\lim_{h\to 0^+}\frac{f(a+h)-f(a)}{h}\]

Variables: \(f'_{-}(a)\) and \(f'_{+}(a)\) are left and right derivatives.

Conditions: \(f\) differentiable at \(a\) iff both exist and are equal.

Piecewise functions, modulus and corner/cusp points.