Find solutions of $2x^3\ge 1-6x^2$ The inital function I want to study is 
$$\frac{x^3+1}{x+2}$$
Its derivative is 
$$\frac{2x^3+6x^2-1}{(x+2)^2}$$
I want to solve the following inequality graphically:
$$2x^3\ge 1-6x^2$$
I tried drawing the graphs of both the functions. But couldn’t find a way to find the minimum $(0,1)$ and maximum $(-1,0)$. Any hints on how to find those points?

Exact solutions with CAS Maxima:
$$2 \cos{\left( \frac{\operatorname{atan}\left( \frac{\sqrt{7}}{3}\right) -3 {\pi} }{3}\right) }-1\le x \le \cos{\left( \frac{\operatorname{atan}\left( \frac{\sqrt{7}}{3}\right) +{\pi} }{3}\right) }-1,$$
$$x \ge \cos{\left( \frac{\operatorname{atan}\left( \frac{\sqrt{7}}{3}\right) -{\pi} }{3}\right) }-1$$
or
$$-2.942241850969666\le x\le  -0.4421253016684752,$$
$$x\ge 0.3843671526381418$$
