Question

函数f(x)=x(1-x^2)在区间[0,1]上的最大值为？

Answer 1

1-x(1-x)=(x-1/2)^2+3/4 大于等于3/4
则f(x)小于等于4/3

Answer 2

F'(X)=(1-X^2)-2X^2=1-3X^2 ,F'(X)=0
1=3X^2 , X=√3/3
0<X<√3/3 , F'(X)>0
√3/3<X<1 , F'(X)<0
F(√3/3)=2√3/9