= One-sided derivative
{title2=$f'_-(a),f'_+(a)$}
The right and left <one-sided derivatives> are the limits of the <difference quotient> restricted respectively to positive and negative increments:
$$
f'_+(a)=\lim_{h\downarrow0}\frac{f(a+h)-f(a)}h,
\qquad
f'_-(a)=\lim_{h\uparrow0}\frac{f(a+h)-f(a)}h.
$$
At an interior point, <differentiability> is equivalent to existence and equality of these two finite limits. For the <absolute value function>, $f'_+(0)=1$ and $f'_-(0)=-1$, so it is continuous at zero but not differentiable there.
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