Question

函数y=根号(x^2-6x+8)(-x^2+6x-5)的最大值

Answer 1

答：

y=√[-(x²-6x+8)(x²-6x+5)]

=√(-[(x²-6x)²+13(x²-6x)+40])

=√(-[(x²-6x+13/2)²+40-169/4])

=√(-[(x²-6x+13/2)²-9/4])

=√(9/4-(x²-6x+13/2)²)

当x²-6x+13/2=0时,y有最大值√9/4=3/2

而x²-6x+13/2=0解为：x=(6±√10)/2.

所以当x满足x²-6x+13/2=0,即x=(6±√10)/2时,y有最大值为3/2.