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Differentiation

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Question 440

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

Differentiation Questions

  1. A Level
  2. /Maths
  3. /Differentiation

717 exam-style questions on Edexcel A Level Maths Differentiation, covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change. Each one has a worked solution and a mark scheme showing where the marks go.

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