Question

使函数y=e的[-(x-1)^2]次方的一阶导数和二阶导数分别为0的x是多少

Answer 1

y'=e^(-(x-1)^2)(-2(x-1))
y'=0得：x-1=0,即x=1
y"=e^(-(x-1)^2) *4(x-1)^2-2e^(-(x-1)^2)
=2e^(-(x-1)^2)[ 2(x-1)^2-1]
y"=0,有：2(x-1)^2-1=0
解得:x=1+√2/2,1-√2/2