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The average value of a continuous function is its integral divided by the interval width — the height of the rectangle with the same area. The mean value theorem for integrals guarantees the function actually attains it somewhere.
Average value
f̄ = (1/(b − a)) ∫ₐᵇ f(x) dx
The integral is 9, divided by 3 gives 3, attained at x = √3 ≈ 1.7320508.
It is the limit of that process as the samples become infinitely dense and evenly spaced.