Question

函数fx=(x-x3)/1+2x2+x4的最大值和最小值的乘积

Answer 1

f(x)＝(x-x³)/(1+2x²+x^4)

＝(1/2)·[2x/(1+x²)]·[(1-x²)/(1+x²)].

设x＝tan(θ/2),则

f(x)＝(1/2)sinθcosθ＝(1/4)sin2θ.

∴f(x)|max＝1/4,f(x)|min＝-1/4.

∴f(x)|max·f(x)|min＝-1/16.