Question

函数f(x)=1/2(e^x+e^-x)的极小值点为

Answer 1

f(x)=1/2(e^x+e^-x)

df/dx = (1/2)[e^x - e^(-x)]

d^2f/d^2x = (1/2)[e^x + e^(-x)] > 0

令 df/dx = 0

得 e^x - e^(-x),e^2x = 1,x = 0

f极小 = (1/2)(1 + 1)=1

答案：极小值为 1,极小值的坐标为 (0,1).