求函数f(x)=x²-2ax+1,x∈[1,3]的最小值.

f(x)
= x² - 2ax + 1
= x² - 2ax + a² + 1 - a²
= (x - a)² + 1 - a²
当 a < 1 时,最小值 = f(1) = -2a + 2
当 a > 3 时,最小值 = f(3) = -6a + 10
当 -1 ≤ a ≤ 3时,最小值 = f(a) = 1 - a²