4PM1/02 Jan 2023, Question 4: Tangents, Normals and Stationary Points (Further)
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 7 marks
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The question, in short
For the curve y = x³ sin x, find the tangent line equation at the point where x = π/2, giving it as y = mx + c.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 7 marks
- 1At x = π/2: y = (π/2)³ × 1 = π³/8
- 2dy/dx = 3x² sin x + x³ cos x
- 3At x = π/2: dy/dx = 3(π/2)² × 1 + 0 = 3π²/4
- 4y − π³/8 = (3π²/4)(x − π/2)
- 5y = (3π²/4)x − 3π³/8 + π³/8
- 6y = (3π²/4)x − π³/4
Answery = (3π²/4)x − π³/4
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