本题目来源于试卷: Differential Calculus，类别为 IB数学
[问答题]
Let $f(x)=\frac{2 x+1}{x-3}$,$ x \in \mathbb{R}$,$ x \neq 3 $
1. a. Find the equation of the vertical and horizontal asymptote of f .
b. Write down the coordinates of the point Q at which the asymptotes intersects.
c. Find the x and y intercepts of f .
2. Show that $f^{\prime}(x)=-\frac{7}{(x-3)^{2}}$ .
3. Hence, find the equation of the tangent at point $\mathrm{P}(4, y) $.
4. The point S also lies on the graph of f . The tangent to S is parallel to the tangent at point P . Find the coordinates of S .
5. Show that Q is the midpoint of [PS].
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