Final answer:
The continuity of a function at a point is related to the existence and equality of the left-hand and right-hand derivatives at that point.
Step-by-step explanation:
The relationship between the continuity of a function at point a and the left-hand derivative (LHD) and right-hand derivative (RHD) at point a is that if a function is continuous at point a, then both the LHD and RHD exist and are equal at that point. This means that the function has a well-defined derivative at that point. Conversely, if the LHD and RHD exist and are equal at point a, then the function is continuous at that point.