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1.6 Differentiation

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Question 49

A curve, representing the vertical cross-section of a high-precision optical lens, has the equation $y = 2x^3 - 96x$ .

The point $P$ on the curve has $x$ -coordinate $4$ .

The point $Q$ on the curve has $x$ -coordinate $4 + h$ .

Show that the gradient of the chord $P Q$ is $2h^2 + 24h$ .

[4]

Explain how the result of part (a) can be used to show that $P$ is a stationary point on the curve.

[2]

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 49

A curve, representing the vertical cross-section of a high-precision optical lens, has the equation $y = 2x^3 - 96x$ .

The point $P$ on the curve has $x$ -coordinate $4$ .

The point $Q$ on the curve has $x$ -coordinate $4 + h$ .

Show that the gradient of the chord $P Q$ is $2h^2 + 24h$ .

[4]

Explain how the result of part (a) can be used to show that $P$ is a stationary point on the curve.

[2]

Markscheme

1.6 Differentiation Questions

A Level
Maths
1.6 Differentiation