Question

当a为何值时,函数f(x)=1\3x^3+(a+2)x^2 +(2a+1)x+1没极值点.

Answer 1

f(x)=13x^3+(a+2)x^2 +(2a+1)x+1

求导,得

f'(x)=x^2+2(a+2)x +2a+1

△=4(a+2)^2-4(2a+1)=4(a^2+4a+4)-8a-4=4a^2+8a+12=4(a+1)^2+8>0

因为没有极值点,所以此时△应