根号下(x➖1)²➕1 加上根号下(5➖x²)的最大值和最小值怎么求 求详细解答过程谢谢
第1个回答 2022-12-15
设f(x)=√[(x-1)^2+1]+√(5-x^2)
=√(x^2-2x+2)+√(5-x^2),(-√5≤x≤√5),
f'(x)=(x-1)/√(x^2-2x+2)-x/√(5-x^2)=0,
(x-1)√(5-x^2)=x√(x^2-2x+2),①
平方得(x^2-2x+1)(5-x^2)=x^2(x^2-2x+2),
整理如下:
x^4-2x^3+2x^2
+x^4-2x^3+x^2
......................-5x^2+10x-5=
2x^4-4x^3-2x^2+10x-5=0,
超出中学数学范围,需要继续吗?
=√(x^2-2x+2)+√(5-x^2),(-√5≤x≤√5),
f'(x)=(x-1)/√(x^2-2x+2)-x/√(5-x^2)=0,
(x-1)√(5-x^2)=x√(x^2-2x+2),①
平方得(x^2-2x+1)(5-x^2)=x^2(x^2-2x+2),
整理如下:
x^4-2x^3+2x^2
+x^4-2x^3+x^2
......................-5x^2+10x-5=
2x^4-4x^3-2x^2+10x-5=0,
超出中学数学范围,需要继续吗?