A Visual Proof: e ≤ A ≤ B ⇒ A^B > B^A.

Fascination with the constants e and π has encouraged numerous visual proofs of the inequality π^e < e^π. Nakhli [4] used the fact that 1/ e is a global maximum for y = ln(x)/ x to conclude the relation, and Nelsen [5] used the fact that y = e^(x/e) lies above the line y = x. Also I [7] have submitted an article in Intelligencer journal on e^A > A^e and it is accepted. Gallant [2] provided the most general proof for which this inequality is a consequence, showing that when e ≤ A < B, we have A^B > B^A; he used slopes of secant lines connecting the origin to points on the curve y = ln(x). We provide an alternate visual proof for this general inequality using an area argument.