October 2021 Paper 2 Q2
2 The diagram shows part of the graph of \(y = \mathrm{f}(x)\), where \(\mathrm{f}(x)\) is a cubic polynomial in \(x\).
Explain why one of the roots of the equation \(\mathrm{f}(x) = 0\) cannot be found by the sign change method. [2]
| Scheme | Marks |
|---|---|
| \(\mathrm{f}(x)\) is positive on both sides of the 1st root oe Curve does not cross the \(x\)-axis (near root) Sign does not change (near the root) No negative value (near the root) | B2 |
| [2] |
Notes
B1 for "The graph touches the \(x\)-axis" or “repeated root” or “It is a stationary point”
Ignore all else, eg “inflection”