OCR MEI C2 — Question 5 5 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicStationary points and optimisation
TypeFind range where function increasing/decreasing
DifficultyModerate -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).
Spec1.07i Differentiate x^n: for rational n and sums1.07n Stationary points: find maxima, minima using derivatives1.07o Increasing/decreasing: functions using sign of dy/dx

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.

Question 5:
AnswerMarks Guidance
AnswerMarks Guidance
\(y' = 3x^2 - 12x - 15\)M1 For two terms correct
Use of \(y' = 0\), s.o.i. ftM1
\(x = 5,\ -1\) c.a.o.A1
\(x < -1\) or \(x > 5\) f.t.A1
[5]
## Question 5:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $y' = 3x^2 - 12x - 15$ | **M1** | For two terms correct |
| Use of $y' = 0$, s.o.i. ft | **M1** | |
| $x = 5,\ -1$ c.a.o. | **A1** | |
| $x < -1$ or $x > 5$ f.t. | **A1** | |
| **[5]** | | |
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]}}