- #1
teetar
- 35
- 0
Homework Statement
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]
Homework Equations
None that I can think of.
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 into start myself off? Thanks for any tips!