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1.10 G: Differentiation

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Question 171

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]
Markscheme

1.10 G: Differentiation Questions

  1. A Level
  2. /Maths
  3. /1.10 G: Differentiation

375 exam-style questions on AQA A Level Maths 1.10 G: Differentiation, covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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