Question

已知函数f(x)=x^3-mx^2-m^2x+m^3/27(m>3/4)

Answer 1

f'(x)=3x^2-2mx-m^2

f(x)取极值

f'(x)=0,x=m,x=-1/3m

取极大值时x=-1/3m

又[-1/3m,m] 在【1,4/3*m】之内

则f'(1)=3-2m-m^2,f'(4/3m)=5/3m^2,f'(x)min=-4/3m^2

要满足|f'(x)|≤4m

则f'(1)≤4m,f'(4/3m)≤4m,|f'(x)min)|≤4m

可以得到m