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1.6 Differentiation

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Question 44

A curve has equation $y = x^3 - 27x$ .

The point $A$ on the curve has $x$ -coordinate $3$ .

The point $B$ on the curve has $x$ -coordinate $3 + h$ .

Show that the gradient of the line $A B$ is $h^2 + 9h$ .

[5]

Explain how the result of part (a) can be used to show that $A$ 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 44

A curve has equation $y = x^3 - 27x$ .

The point $A$ on the curve has $x$ -coordinate $3$ .

The point $B$ on the curve has $x$ -coordinate $3 + h$ .

Show that the gradient of the line $A B$ is $h^2 + 9h$ .

[5]

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

[2]

Markscheme

1.6 Differentiation Questions

A Level
Maths
1.6 Differentiation