Evidence for Minimum Age:

• David had single-handedly killed a lion and a bear while tending sheep
• He was described as a "mighty and valiant man of war"
• He became Saul's armor-bearer in training
• He was of sufficient size to try on Saul's armor
• Jonathan gave David his weapons and clothes, suggesting David was fully grown
• The context of Saul offering his daughter in marriage implies David was of marriageable age

Evidence for Maximum Age:

• Biblical norm called for males 20 and older to serve in the army
• David was not with the army, but tending sheep
• Eliab's remarks suggest David was not expected to be at the battle
• David came to the battle scene without weapons of war

Reconciling the Age of David's Brothers:

Various scenarios are proposed to explain why only three of David's older brothers were in the army, including:

• One brother may have died young
• Possibility of twins or triplets
• Illness, recent marriage, or other exemptions from military service

Conclusion:

Based on the biblical evidence and logical deductions, we conclude that David was approximately 18 years old when he slew Goliath. This age fits with him being physically mature but not yet of full military age (20), while also aligning with descriptions of him as a "youth" but capable of significant military feats.