Question 2 - A-Level Maths

Edexcel C2 — Question 2 5 marks

Exam Board	Edexcel
Module	C2 (Core Mathematics 2)
Marks	5
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Stationary points and optimisation
Type	Find range where function increasing/decreasing
Difficulty	Moderate -0.3 This is a straightforward C2 differentiation application requiring students to find f'(x), set it greater than zero, and solve a quadratic inequality. While it involves multiple steps (differentiate, factorise/use quadratic formula, determine sign), these are all standard techniques with no conceptual challenges, making it slightly easier than average.
Spec	1.07o Increasing/decreasing: functions using sign of dy/dx

2. $$f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - 3 x + 7$$ Find the set of values of $x$ for which $\mathrm { f } ( x )$ is increasing.

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Question 2:

Answer	Marks	Guidance
Answer/Working	Marks	Notes
$f'(x) = 3x^2 + 8x - 3$	M1 A1
increasing when $3x^2 + 8x - 3 \geq 0$	M1
$(3x-1)(x+3) \geq 0$	M1
$x \leq -3$ or $x \geq \frac{1}{3}$	A1	(5)

## Question 2:

| Answer/Working | Marks | Notes |
|---|---|---|
| $f'(x) = 3x^2 + 8x - 3$ | M1 A1 | |
| increasing when $3x^2 + 8x - 3 \geq 0$ | M1 | |
| $(3x-1)(x+3) \geq 0$ | M1 | |
| $x \leq -3$ or $x \geq \frac{1}{3}$ | A1 | **(5)** |

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2.

$$f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - 3 x + 7$$

Find the set of values of $x$ for which $\mathrm { f } ( x )$ is increasing.\\

\hfill \mbox{\textit{Edexcel C2  Q2 [5]}}

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