In this question:-The child is 3 years old History of Asthma in mother Extensor involvementFirst two points suggest the diagnosis of atopic dermatitis (childhood pattern). About third point (extensor involvement) :-"Though childhood atopic dermatitis mainly involves flexural parts, less commonly extensor surfaces may also be involved".Further, you can easily rule out other three options:-Contact dermatitisThe family history of asthma is not important. No history of contact to an allergen.Seborrheic dermatitisOccurs in adults and less frequently in infants but not in children.Infantile eczematous dermatitisOccurs in Infant.