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$\huge y=a \cdot x^3 + b \cdot x^2 + c \cdot x + d$
$\huge y'=3a \cdot x^2 + 2b \cdot x + c$
$\huge y''=6a \cdot x + 2b$
$\huge y''=0 @ x=-\frac{b}{3a}$
$\huge y'=0 @ x=-\frac{b}{3a} \pm \frac{\sqrt{b^2-3ac}}{3a}$
$\huge y'=0 @ x=-\frac{b}{3a} \pm \sqrt{\left(\frac{b}{3a}\right)^2-\frac{c}{3a}}$
Location x where $\huge y' = -y' @ y''=0 @ x=-\frac{b}{3a}$
$\huge y' = -y' @ y''=0 @ x=-\frac{b}{3a} @ x=-\frac{b}{3a} \pm \sqrt{2\left[\left(\frac{b}{3a}\right)^2-\frac{c}{3a}\right]}$