Moderate -0.5 This is a straightforward application of differentiation to find stationary points by setting dy/dx = 0, solving a quadratic, then using the second derivative or sign test to determine where the function is increasing. It's slightly easier than average because it involves routine calculus techniques with no conceptual challenges, though it requires multiple steps (differentiate, solve quadratic, analyze intervals).
5 Use calculus to find the \(x\)-coordinates of the turning points of the curve \(y = x ^ { 3 } - 6 x ^ { 2 } - 15 x\). Hence find the set of values of \(x\) for which \(x ^ { 3 } - 6 x ^ { 2 } - 15 x\) is an increasing function.
5 Use calculus to find the $x$-coordinates of the turning points of the curve $y = x ^ { 3 } - 6 x ^ { 2 } - 15 x$. Hence find the set of values of $x$ for which $x ^ { 3 } - 6 x ^ { 2 } - 15 x$ is an increasing function.
\hfill \mbox{\textit{OCR MEI C2 Q5 [5]}}