Heres some quality problem solving for anyone who wishes to have a go
A sine function is such that when u differentiate it, the resulting function has an amplitude twice the original function. If the original function passes through (PI/6,0) and the derivative passes through (7PI/6,0) find a possible sine function.
I'm not sure how general a "sine function" can be, but I'll try this: A*sin(B+C*x).
The first condition implies that C=2.
The second condition implies that sin(B+Pi/3)=0, so B+Pi/3=2*Pi*n for any integer n; I'll try n=0, so B=-Pi/3.
The third condition implies that 0=2A*cos(7Pi/3-Pi/3)=2A*cos(2*Pi)=2A, so A=0.
Therefore, the ONLY possibility is the zero function.
In general, when you have N parameters and N conditions, the parameters are uniquely determined by the conditions.