4PM1/01 Jun 2021, Question 9: Tangents, Normals and Stationary Points (Further)
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 5 marks
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The question, in short
For the curve y = (x³ − 2x)e^(1 − x), determine the equation of the normal line at the point (1, −1).
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Solution · 5 marks
- 1dy/dx = −(x³ − 2x)e^(1 − x) + (3x² − 2)e^(1 − x)
- 2At x = 1: dy/dx = −(−1)(1) + (1)(1) = 2
- 3Gradient of normal = −1/2
- 4y + 1 = −(1/2)(x − 1)
Answery + 1 = −(1/2)(x − 1) (y = −x/2 − 1/2)
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