General 3rd degree polynomial always increasing problem? Please Help!!! What conditions on a, b, and c will make f(x)=ax^3+bx^2+cx+d always increasing? For a function to be always increasing, the first derivative has to be always positive. So, f1(x)=3ax^2+2bx+c>0 I tried finding the roots, that didn't lead me anywhere. Could someone please help? I know that for a 3rd degree polynomial to be always increasing, it has to be a perfect cube. like (ex-f)^3, then you can expand that to be (ex)^3 -3f(ex)^2+3exf^2+f^3. Then since this will have to be the formula for f(x). So a=e^3, b=-3fe^2, c=3ef^2, d=f^3, but i don't know what to do from here. Please help!!!