求曲线 $y=\dfrac{\mathrm{e}^{3x^2-1}}{1-x^2}$ 的各驻点的精确坐标。

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。

用商法则求导，提出恒正的指数因子，再解分子为零。代回函数前确认各根不等于 $\pm1$。

For $x\ne\pm1$, the quotient rule gives

At a stationary point the derivative is zero. Since the exponential is positive,

Hence

All three values are in the domain. At $x=0$, $y=e^{-1}$. At either of the other values, $x^2=4/3$, so

Thus the stationary points are