[填空题]
$\text { The diagram below shows the graph of } f(x)=a \sin (k(x-d))+c \text {, for } 2 \leq x \leq 14 \text {. }$
The graph of f has a maximum at $\mathrm{P}(5,15)$ and a minimum at $\mathrm{Q}(11,-5)$ .
1. Write down the value of:
a. a ;
b. c .
2. a. Show that $k=\frac{\pi}{6}$ .
b. Find the smallest possible value of d , given d>0 .
3. Find $f^{\prime}(x)$ .
4. At a point R , the gradient is $-\frac{5 \pi}{3}$ . Find the x -coordinate of R .
