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Bring all terms to the left and factor the quadratic polynomial:Its leading coefficient is positive, so it is nonpositive between its two polynomial roots, including the endpoints. Therefore

The gradient components areAway from the vertical axis, $x\ne 0$, so $u_y=0$ forces $y=0$. The other stationary point equation then gives $x^2=3/2$. Therefore the two requested points areEvery point with $x=0$ also has zero gradient, but those points are explicitly excluded.