N2012 P2 Q3

It is given that \(f(x)=x^3+x^2-2x-4\).

1. Sketch the graph of \(y=f(x)\).[1]
2. Find the integer solution of the equation \(f(x)=4\), and prove algebraically that there are no other real solutions.[3]
3. State the integer solution of the equation \((x+3)^3+(x+3)^2-2(x+3)-4=4\).[1]
4. Sketch the graph of \(y=|f(x)|\).[1]
5. Write down two different cubic equations which between them give the roots of the equation \(|f(x)|=4\). Hence find all the roots of this equation.[4]