1. The problem statement, all variables and given/known data The cubic curve [itex] y = 8x^3 + bx^2 + cx + d[/itex] has two distinct points P and Q, where the gradient is zero. Show that [itex] b^2 > 24c[/itex] 2. Relevant equations None that I can think of. 3. The attempt at a solution There's two distinct points where the gradient is zero, since it's third degree these must be the local maximum and minimums points. I graphed the equation using an online graphing tool and some sliders, and saw that it was in fact true that [itex] b^2 [/itex] has to be greater than [itex]24c[/itex] for there to be these points with zero gradient, but I'm completely lost on how to show this mathematically. What direction should I go in to start myself off? Thanks for any tips!