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1.10.4 Product, quotient and chain rules (A-level only)

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Question 88

A curve has equation y=x3−27xy = x^3 - 27xy=x3−27x.

The point AAA on the curve has xxx-coordinate 333.

The point BBB on the curve has xxx-coordinate 3+h3 + h3+h.

a.

Show that the gradient of the line ABABAB is h2+9hh^2 + 9hh2+9h.

[5]
b.

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

[2]

1.10.4 Product, quotient and chain rules (A-level only) Questions

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