**Core Concept**

The question is asking about the crucial fatty acid found in breast milk that plays a vital role in supporting the growth of infants. Fatty acids are essential components of cell membranes, hormones, and signaling molecules, and they contribute to brain development in infants. In this context, we are specifically focusing on the role of fatty acids in infant growth.

**Why the Correct Answer is Right**

The correct answer, **DHA (docosahexaenoic acid)** is the essential fatty acid that is crucial for infants' growth and development. DHA is a polyunsaturated fatty acid (PUFA) belonging to the omega-3 family, which is essential for proper brain development, visual function, and reducing inflammation in infants. Breast milk contains higher levels of DHA compared to formula milk, which explains its importance for breastfed infants.

**Why Each Wrong Option is Incorrect**

Option A (**Arachidonic acid**) is also an essential fatty acid, but it belongs to the omega-6 family and plays a role in modulating inflammation and immune responses. Although arachidonic acid is present in breast milk, its significance is secondary to DHA.

Option B (**Palmitic acid**) is a saturated fatty acid, which is not an essential fatty acid and is not as crucial for infant growth and development as DHA and arachidonic acid.

Option C (**Olive oil**) is a source of monounsaturated fatty acids, such as oleic acid, which is not as vital as DHA and arachidonic acid in infants. Olive oil is not a suitable alternative to breast milk for infant nutrition.

**Clinical Pearl / High-Yield Fact**

Infants' nutritional requirements differ from adults, and breast milk provides a balanced profile of essential fatty acids, vitamins, and minerals necessary for optimal infant growth and development. Synthetic formulas have been developed to mimic breast milk more closely but cannot replicate the complex combination of nutrients found in breast milk. DHA is just one example of the numerous essential components in breast milk that contribute to infants' overall health and development.

**Correct Answer Explanation**

DHA is the correct answer because it is a critical component of breast milk that supports brain and visual development in infants. As compared to other options, DHA has been shown to have higher concentrations in breast milk, making it a key component in breast milk-fed infants' growth and development.