[填空题]
Let $f(x)=16-x^{2}$ , for x $\in \mathbb{R}$ .
1. Find the x -intercepts of the graph of f .
The following diagram shows part of the graph of f .
Rectangle $\mathrm{ABCD}$ is drawn with $\mathrm{A} \& \mathrm{~B}$ on the x -axis and $\mathrm{C} \& \mathrm{D}$ on the graph of f .
Let $\mathrm{OA}=a$ . P (a,b) a = b = Q (c,d) c = d =
2. Show that the area of $\mathrm{ABCD}$ is 32 a-2 $a^{3}$ .
3. Hence find the value of a>0 such that the area of ABCD is a maximum.
Let $g(x)=(x-4)^{2}+k$ , for x $\in \mathbb{R}$ , where k is a constant. $\frac{a \sqrt{b}}{c}$ a = b = c =
4. Show that when the graphs of f and g intersect, $2 x^{2}-8 x+k=0$ .
5. Given that the graphs of f and g intersect only once, find the value of k .
