Question

已知函f(x)=(1/3)x^3-2x=1,设函数g(x)=-3f(x)+mx^2-6x(m∈R),当x∈[0,1]时,

Answer 1

g(x)=-x^3+6x-3+mx^2-6x

=-x^3+mx^2-3

g'(x)=3x^2+2mx

为开口向上的抛物线,对称轴x=-m/3

已知Ig'(x)I≤1,即-1≤g'(x)≤1

1. -m/30时 g'(x)单增

所以g'(0)=0≥-1 g'(1)=3+2m≤1

解得m≤-1 不成立

2. -m/3>1 即m