Question

已知A（2,2）,B（4,1）,在x轴上有一动点M,向量AM*向量BM取最小值时点M的坐标是

Answer 1

M(x,0)

S= AM.BM

=(x-2,-2).(x-4,-1)

=(x-2)(x-4)+2

= x^2-6x+10

= (x-3)^2 + 1

min S =1 at x=3

M(3,0)