2025 SJI P1 Q4

The following diagram shows the curve \(y=a\sin(b(x-c))+d\) for \(-1\leq x\leq5\), where \(a,b,c\) and \(d\) are positive constants. The curve has a maximum point at \(\left(\dfrac32,\dfrac{11}2\right)\) and a minimum point at \(\left(\dfrac52,\dfrac12\right)\).

1. Find the value of \(a\) and the value of \(d\).[3]
2. Find the value of \(b\).[2]
3. Find the smallest possible value of \(c\).[2]