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1.9.15 Rates of change with the chain rule (A-level only)

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Question 12

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

1.9.15 Rates of change with the chain rule (A-level only) Questions

A Level
Maths
1.9.15 Rates of change with the chain rule (A-level only)

24 exam-style questions on OCR (MEI) A Level Maths 1.9.15 Rates of change with the chain rule (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

1.9.15 Rates of change with the chain rule (A-level only)

Question bank

1.9.15 Rates of change with the chain rule (A-level only)

Medium Hard

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Question 12

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

1.9.15 Rates of change with the chain rule (A-level only) Questions

A Level
Maths
1.9.15 Rates of change with the chain rule (A-level only)

24 exam-style questions on OCR (MEI) A Level Maths 1.9.15 Rates of change with the chain rule (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.