Finding the maximum value of function f (x) = x2-2ax + 1 x ∈ [1,3]

F (x) = x & sup2; - 2aX + 1F (x) = (x-a) & sup2; + 1-A & sup2; this function is a quadratic function with the opening upward. The axis of symmetry is x = A. when a ≤ 1, X ∈ [1,3] f (x) is an increasing function. The maximum value is f (3) = 10-6a, and the minimum value is f (1) = 2-2a. When 1 ≤ a ≤ 2, the distance between X = 3 and the axis of symmetry is farther than that of x = 1, so f (3) > F (1)

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