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WMA11/01 Oct 2020, Question 8: Differentiating Polynomials

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 11 marks

The question, in short

For curve y = (x − 2)(x − 4)², differentiate, find tangent at x = 6, and find x-value where a parallel distinct tangent touches.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 4 marks

Show the derivative of y = (x − 2)(x − 4)² equals 3x² − 20x + 32.

  1. 1y = (x − 2)(x² − 8x + 16)
  2. 2= x³ − 8x² + 16x − 2x² + 16x − 32
  3. 3= x³ − 10x² + 32x − 32
  4. 4dy/dx = 3x² − 20x + 32

AnswerShown: y = x³ − 10x² + 32x − 32, so dy/dx = 3x² − 20x + 32

Part (b) · 4 marks

Find the tangent line to C at x = 6, in the form y = mx + c.

  1. 1At x = 6: y = (6 − 2)(6 − 4)² = 16
  2. 2dy/dx = 3(36) − 20(6) + 32 = 20
  3. 3y − 16 = 20(x − 6)
  4. 4y = 20x − 104

Answery = 20x − 104

Part (c) · 3 marks

Given tangents at x = 6 and x = α are parallel and distinct, find α.

  1. 1Parallel tangents have the same gradient: 3x² − 20x + 32 = 20
  2. 23x² − 20x + 12 = 0
  3. 3(3x − 2)(x − 6) = 0
  4. 4x = 6 gives l₁ itself, so α = 2/3

Answerα = 2/3

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Also searched as: WMA11 October 2020 · WMA11/01 · wma11 oct20 · IAS Maths Pure Mathematics 1 October 2020 · question 8.
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