Question

求函数f（x）=x^2-2mx+m^2,在[-1,1]上的最大值与最小值

Answer 1

函数f（x）=x^2-2mx+m^2=(x-m)^2,其中x∈(-1,1),

(1)当m∈(-∞,-1)时,f(x)最大值为f(1)=(1-m)^2,

f(x)最小值为f(-1)=(-1-m)^2=(1+m)^2

(2)当m∈[-1,0]时,f(x)最大值为f(1)=(1-m)^2,

f(x)最小值为f(m)=0

(3)当m∈[0,1]时,f(x)最大值为f(-1)=(-1-m)^2=(1+m)^2

f(x)最小值为f(m)=0

(4)当m∈(1,+∞)时,f(x)最大值为f(-1)=(-1-m)^2=(1+m)^2,

f(x)最小值为f(1)=(1-m)^2