Moderate -0.8 This is a straightforward differentiation question requiring students to find dy/dx = 9x² - 12x + 4, then show it's always non-negative by completing the square or using the discriminant. It's a standard technique with clear method and minimal steps, making it easier than average but not trivial since it requires recognizing how to prove non-negativity of a quadratic.
2 A curve has equation $y = 3 x ^ { 3 } - 6 x ^ { 2 } + 4 x + 2$. Show that the gradient of the curve is never negative.
\hfill \mbox{\textit{CAIE P1 2011 Q2 [3]}}