[问答题]
$\text { Let } f(x)=x^{2}-3 x+2 \text {, for } x \in \mathbb{R} \text {. The following diagram shows part of the graph of } f \text {. }$
The graph of f crosses the x -axis at the point $\mathrm{P}(1,0)$ and at the point $\mathrm{Q}(2,0)$ .
1. Show that $ f^{\prime}(1)=-1$ .
The line L is the normal to the graph of f at P .
2. Find the equation of L in the form y=m x+c .
The line L intersects the graph of f at another point R , as shown in the following diagram.
3 . Find the x -coordinate of R .
4. Find the area of the region enclosed by the graph of f and the line L .
