2025 ESSS P2 Q9

The diagram shows the curve \(y=x^3+3x^2-4x\) cuts the \(x\) axis at points \(O\), \(E\) and \(F\). The line \(y=-4x+4\) is the tangent to the curve at point \(G\) which meets the curve again at \(F\).

1. Find the coordinates of \(E\) and \(F\).[4]
2. Find the gradient function of the curve.[1]
3. Hence, show that the \(x\)-coordinate of \(G\) is \(-2\).[3]
4. Calculate the area of the shaded region.[4]