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WMA11/01 Oct 2019, Question 7: The Derivative as a Limit

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 6 marks

The question, in short

For the curve y = 2x² + 5 with point P(2, 13), work out the tangent gradient at P, the gradient of chord PQ where Q has x = 2 + h, and link the two results.

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

Part (a) · 2 marks

Work out the slope of the tangent line touching the curve at the point P(2, 13).

  1. 1dy/dx = 4x
  2. 2At x = 2: gradient = 8

Answer8

Part (b) · 3 marks

Using Q at x = 2 + h on the curve, work out the slope of line PQ in terms of h, fully simplified.

  1. 1y at Q = 2(2 + h)² + 5 = 2(4 + 4h + h²) + 5 = 13 + 8h + 2h²
  2. 2Gradient PQ = (13 + 8h + 2h² − 13) ÷ (2 + h − 2)
  3. 3= (8h + 2h²)/h = 8 + 2h

Answer8 + 2h

Part (c) · 1 mark

State briefly how the slope found in part (b) connects to the tangent slope found in part (a).

  1. 1As h → 0, Q moves towards P and 8 + 2h → 8
  2. 2So the limit of the chord gradient equals the tangent gradient 8 from (a)

AnswerAs h → 0, the gradient of PQ (8 + 2h) tends to 8, the gradient of the tangent at P

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Also searched as: WMA11 October 2019 · WMA11/01 · wma11 oct19 · IAS Maths Pure Mathematics 1 October 2019 · question 7.
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