[填空题]
Let f(x)=a sin (k(x-d))+p 2+rll:hw(73ncw k/f 1ypkbg v,jyr,c3tjk b/r1xdf/ , for $1 \leq x \leq 7$.
The graph of f is shown on the diagram below.
The graph of f has a maximum at $ \mathrm{A}(2,5) $ and a minimum at $\mathrm{B}(4,1)$ .
1. Find the value of:
1. a ;
2. c.
2. 1. Find the value of k .
2. Find the smallest possible value of d , given d>0 .
The graph of f is translated by a vector $\binom{0}{b}$ to give the graph of a function g such that g(x)=3 has only one solution in the given domain.
3. Find the value of b .
