U guys are thinking too much. well how does F(x)=A.X behave ( it is either increasing ORdecreasing From + infinity to - infinity) depending upon the sign of A Similarly, How does F(X)=B.X^2 behave( its a parabola right so its increasing AND then decreasing or vice versa depending upon the sign of B) Furthermore, how does F(x)=C.X^3 behave. It is also increaseing OR decreasing from + infinity to negative infinity depending upon the sign of C. This is becuase it will always have a infletion (ogee) point. Now to the question. From the given information it should be obvious that the condition need to hold for A.x^3+B.X^2+C.X+D is A+C-B>0 because this condition will over power how the X^2 behaves. P.s D does not matter because it just shifts the intercept. I think that is the condition needed for the function to be increasing or decreasing from negative infinity to positive infinity. Best of Luck.