Very young babies demonstrate frustration when they are struggling to complete a developmentally difficult task or when they are prevented from completing an action. Anger, identified by facial expressions and cries that differ from those of frustration, may emerge at around 4 months when an infant is having difficulty completing a task or getting the attention of an adult. Although one may see indications of frustration right from birth, the unique expressions associated with anger are frequently reported to begin at around 4 months. Other researchers have suggested that babies as young as 2 months old may show anger.
References:
Lewis, M. (2000). The emergence of human emotions. In Lewis, M., & Haviland-Jones, J. M. (Eds.), Handbook of emotions (2nd ed.). New York: Guilford Press.
Lewis, M., Alessandri, S., & Sullivan, M. W. (1990). Violation of expectancy, loss of control, and anger in young infants. Developmental Psychology, 26, 745