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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=2x3−96xy = 2x^3 - 96xy=2x3−96x.

The point PPP on the curve has xxx-coordinate 444.

The point QQQ on the curve has xxx-coordinate 4+h4 + h4+h.

a.

Show that the gradient of the chord PQPQPQ is 2h2+24h2h^2 + 24h2h2+24h.

[4]
b.

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

[2]

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

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