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1.6 Differentiation

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Question 31

A curve $C$ has equation

2x^3 - 15x + \frac{k}{x}, \quad x > 0

where $k$ is a constant. The point $P$ with $x$ -coordinate $1$ lies on $C$ . Given that $P$ is a stationary point of $C$ :

show that $k = - 9$ .

[3]

Determine the nature of the stationary point at $P$ , justifying your answer.

[3]

The curve $C$ has a second stationary point.

Using algebra, find the $x$ -coordinate of this second stationary point.

[4]

Markscheme

1.6 Differentiation Questions

A Level
Maths
1.6 Differentiation

115 exam-style questions on CCEA A Level Maths 1.6 Differentiation, covering 1.6.1 Differentiation, 1.6.2 Differentiation, 1.6.3 Differentiation, 1.6.4 Differentiation, 1.6.5 Differentiation, 1.6.6 Differentiation, and 1.6.7 Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.

1.6 Differentiation

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1.6 Differentiation

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Question 31

A curve $C$ has equation

2x^3 - 15x + \frac{k}{x}, \quad x > 0

where $k$ is a constant. The point $P$ with $x$ -coordinate $1$ lies on $C$ . Given that $P$ is a stationary point of $C$ :

show that $k = - 9$ .

[3]

Determine the nature of the stationary point at $P$ , justifying your answer.

[3]

The curve $C$ has a second stationary point.

Using algebra, find the $x$ -coordinate of this second stationary point.

[4]

Markscheme

1.6 Differentiation Questions

A Level
Maths
1.6 Differentiation