Moderate -0.5 This question tests conceptual understanding of when sign change methods fail (at repeated roots where the graph touches but doesn't cross the x-axis), but requires only recognition of this standard limitation rather than any calculation or problem-solving. It's easier than average as it's purely conceptual recall applied to a given diagram.
2 The diagram shows part of the graph of \(y = \mathrm { f } ( x )\), where \(\mathrm { f } ( x )\) is a cubic polynomial in \(x\).
\includegraphics[max width=\textwidth, alt={}, center]{7298e7b9-ad52-480c-bc2b-8289aeab9ebb-04_437_620_909_274}
Explain why one of the roots of the equation \(\mathrm { f } ( x ) = 0\) cannot be found by the sign change method.
\(f(x)\) 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
B1 for "The graph touches the \(x\)-axis" or "repeated root" or "It is a stationary point". Ignore all else, eg "inflection"
## Question 2:
| Answer | Mark | Guidance |
|--------|------|----------|
| $f(x)$ 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** | B1 for "The graph touches the $x$-axis" or "repeated root" or "It is a stationary point". Ignore all else, eg "inflection" |
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2 The diagram shows part of the graph of $y = \mathrm { f } ( x )$, where $\mathrm { f } ( x )$ is a cubic polynomial in $x$.\\
\includegraphics[max width=\textwidth, alt={}, center]{7298e7b9-ad52-480c-bc2b-8289aeab9ebb-04_437_620_909_274}
Explain why one of the roots of the equation $\mathrm { f } ( x ) = 0$ cannot be found by the sign change method.
\hfill \mbox{\textit{OCR H240/02 2021 Q2 [2]}}