Moderate -0.3 This question requires finding a second derivative by differentiating a polynomial (straightforward), then applying standard criteria for stationary points (dy/dx = 0) and inflection points (d²y/dx² = 0). While it involves two concepts together, both are routine C2-level techniques with no problem-solving insight required, making it slightly easier than average.
6 A curve has gradient given by \(\frac { \mathrm { d } y } { \mathrm {~d} x } = x ^ { 2 } - 6 x + 9\). Find \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\).
Show that the curve has a stationary point of inflection when \(x = 3\).
6 A curve has gradient given by $\frac { \mathrm { d } y } { \mathrm {~d} x } = x ^ { 2 } - 6 x + 9$. Find $\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }$.\\
Show that the curve has a stationary point of inflection when $x = 3$.
\hfill \mbox{\textit{OCR MEI C2 2006 Q6 [4]}}