Standard +0.8 This question tests understanding of inflection points beyond standard textbook definitions. Students must recognize that f''(7)=0 is necessary at an inflection point, while f'(7) can be zero or non-zero. This requires conceptual understanding rather than routine application, making it moderately challenging but still within typical A-level scope.
2 A curve has equation \(y = \mathrm { f } ( x )\)
The curve has a point of inflection at \(x = 7\)
It is given that \(\mathrm { f } ^ { \prime } ( 7 ) = a\) and \(\mathrm { f } ^ { \prime \prime } ( 7 ) = b\), where \(a\) and \(b\) are real numbers.
Identify which one of the statements below must be true.
Circle your answer.
\(\mathrm { f } ^ { \prime } ( 7 ) \neq 0\)
\(\mathrm { f } ^ { \prime } ( 7 ) = 0\)
\(\mathrm { f } ^ { \prime \prime } ( 7 ) \neq 0\)
\(\mathrm { f } ^ { \prime \prime } ( 7 ) = 0\)
2 A curve has equation $y = \mathrm { f } ( x )$
The curve has a point of inflection at $x = 7$\\
It is given that $\mathrm { f } ^ { \prime } ( 7 ) = a$ and $\mathrm { f } ^ { \prime \prime } ( 7 ) = b$, where $a$ and $b$ are real numbers.
Identify which one of the statements below must be true.\\
Circle your answer.\\
$\mathrm { f } ^ { \prime } ( 7 ) \neq 0$\\
$\mathrm { f } ^ { \prime } ( 7 ) = 0$\\
$\mathrm { f } ^ { \prime \prime } ( 7 ) \neq 0$\\
$\mathrm { f } ^ { \prime \prime } ( 7 ) = 0$
\hfill \mbox{\textit{AQA Paper 2 2021 Q2 [1]}}