Problem of the Week
Problem E
Mystery Function

For some function \(f(x)=ax^3+bx^2+cx+d\), where \(a\), \(b\), \(c\), and \(d\) are integers, we know the following information:

• the \(y\)-intercept is \(5\),

• \(f(2)=-3\),

• \(f(4)\) is greater than \(40\) but less than \(50\), and

• \(f(6)\) is greater than \(240\) but less than \(250\).

Determine the value of \(f(7)\).