2025 AHS PRELIMS P2 Q13

The graph of \(y=\dfrac17x^3-x^2+\dfrac12x+3\) is drawn on the grid.

Using your graph,

1. write down the range of values of \(x\) such that \(y\geq2\).[1]
2. find the gradient of the tangent to the curve where \(x=-0.5\).[2]
3. by drawing a suitable straight line on the grid, solve the equation \(6x^3-42x^2+126=21x\).[3]

For (a) and (c), extend the grid beyond \(x=7.1\) and \(y=7.1\) to include the third intersection with the additional line. The supplied window clips that intersection.