WMA11/01 Oct 2021, Question 2: Differentiating Roots and Fractional Powers
Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 5 marks
The question, in short
For the curve y = 3x⁵ + 4x³ − x + 5, find the x coordinates of points P and Q where the gradient equals 2, showing full working without calculator methods.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 5 marks
- 1dy/dx = 15x⁴ + 12x² − 1
- 215x⁴ + 12x² − 1 = 2, so 15x⁴ + 12x² − 3 = 0
- 3Divide by 3: 5x⁴ + 4x² − 1 = 0
- 4(5x² − 1)(x² + 1) = 0, so x² = 1/5 (x² = −1 has no real roots)
- 5x = ±1/√5
Answerx = 1/√5 and x = −1/√5 (±√5/5)
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