Final answer:
Infants usually begin to demonstrate meaningful social smiles at the usual initial age of approximately 2 months, aligning with the period when they develop better control of their head and begin cooing and babbling at familiar individuals.
Step-by-step explanation:
The usual initial age at which infants begin to demonstrate meaningful social smiles in response to parental interaction is typically around 2 months of age. During the first two months after birth, an infant normally develops the ability to hold their head erect and steady and to roll from their side to their back. It is around this time that they are likely to start cooing, babbling at their parents, and also smiling at their parents.
These smiles represent an important social development milestone and signal the infant's increasing engagement with their environment and with caregivers. Social smiling is a part of the infant's emotional development and communication skills. It reflects the baby's recognition of their parents and their growing emotional bond.
Therefore, the correct answer to the question is a. 2 months. This is the usual initial age where we might expect to observe these meaningful social interactions with infants.