4MA1/1H Jun 2020, Question 23: Gradient of a Curve at a Point
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 4 marks
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The question, in short
For the cubic y = px³ − mx with p and m positive integers, find the x-values, in terms of p and m, where the curve's gradient is negative.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 4 marks
- 1dy/dx = 3px² − m
- 2Negative gradient: 3px² − m < 0
- 3x² < m/(3p)
- 4−√(m/(3p)) < x < √(m/(3p))
Answer−√(m/(3p)) < x < √(m/(3p))
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