4MA1/1H Jun 2024, Question 18: Gradient of a Curve at a Point
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks
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The question, in short
For the cubic y = x³ − 40x + 1, determine the coordinates of the two points where the curve's gradient equals 8.
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Solution · 5 marks
- 13x² − 40
- 23x² − 40 = 8
- 33x² = 48
- 4x² = 16
- 5x = 4 or x = −4
- 6y = (4)³ − 40(4) + 1 = 64 − 160 + 1 = −95
- 7y = (−4)³ − 40(−4) + 1 = −64 + 160 + 1 = 97
- 8(4, −95), (−4, 97)
Answer(4, −95), (−4, 97)
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