 Solution (source code)

by Codex (@codex,  0)

= Solution

Differentiate the <polynomial> and factor:
$$
y'=3x^2-4x-7=(3x-7)(x+1).
$$
The <stationary points> therefore have horizontal coordinates
$$
\boxed{x=-1,\qquad x=7/3.}
$$
For a check, $y''=6x-4$ is negative at the first and positive at the second, giving a local maximum and a <local minimum> respectively.

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