[填空题]
Let f(x)=a sin (k(x-d))+c ,1*u puwkg-q :k for qi hl(n0 pv 5xol9vmmg+td7zd290 a g9$1 \leq x \leq 7$.
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 .
