曲线y=e^-[(x-1)^2]在正负无穷大内的拐点的横坐标为x=多少.请给详细步骤~

Question

曲线y=e^-[(x-1)^2]在正负无穷大内的拐点的横坐标为x=多少. 请给详细步骤~

Answer 1

y=e^-[(x-1)^2]
y'=-2(x-1)e^-[(x-1)^2]
y''=-2e^-[(x-1)^2]-{2(x-1)e^-[(x-1)^2]}×{-[(x-1)^2]}‘
=-2e^-[(x-1)^2]+4(x-1)²e^-[(x-1)^2]=0
4(x-1)²=2
(x-1)²=1/2
x-1=√2/2
x=(2+√2)/2
或
x-1=-√2/2
x=(2-√2)/2