As for 0 and-1, the derivative function G (x) = 2ax 2+A+ 1 is analyzed.

δ=-8a(a+ 1)

If a=0 or-1, δ = 0 (according to this discriminant analysis)

Therefore, there are:

When a≥0 and δ ≤ 0, the derivative function has no zero point upward, and g(x) is always greater than 0, thus increasing monotonically;

When a≤- 1 and δ≤ 0, the derivative function has no zero point downward, and g(x) is always less than 0, monotonically decreasing;

When-1 < a < 0, δ > 0, the derivative function has two zeros, thus solving g(x)=0, x 1=. . . x2= .。 . At this time, it is difficult to type those numbers by analyzing the monotonicity of the original function in detail, so I can't figure it out.