用反证法证明方程

所表示的曲线没有驻点。

按反证法，先假设曲线存在驻点，因此在某个实数 $x$ 处导数为 $0$。求导并整理后，会得到 $\sin x=3x^2+2$；但右边至少为 $2$，与正弦函数的值域矛盾。

Assume, for a contradiction, that the curve has a stationary point for some real value of $x$. Then

Differentiating,

Therefore, at the assumed stationary point,

However, $x^2\geq0$, so

whereas $\sin x\leq1$ for every real $x$. This is a contradiction.

Hence the original assumption is false, and the curve has

也可以直接给导数设下界；仍使用上面“存在驻点”的反证假设。因为 $3x^2\geq0$ 且 $\sin x\leq1$，

At the assumed stationary point, this contradicts $\frac{\mathrm{d}y}{\mathrm{d}x}=0$. Hence there are no stationary points.