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WMA11/01 Jan 2020, Question 9: Differentiating Roots and Fractional Powers

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 6 marks

The question, in short

Differentiate y = (4x² + 9)/(2√x) for x > 0 without a calculator and find the x coordinate where dy/dx = 0.

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Solution · 6 marks

  1. 1Divide each term by 2x^(1/2): y = 2x^(3/2) + (9/2)x^(−1/2)
  2. 2Differentiate: dy/dx = 3x^(1/2) − (9/4)x^(−3/2)
  3. 3Set dy/dx = 0: 3x^(1/2) = (9/4)x^(−3/2)
  4. 4Multiply by x^(3/2): 3x² = 9/4, so x² = 3/4
  5. 5x > 0, so x = √3/2

Answerx = √3/2

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Also searched as: WMA11 January 2020 · WMA11/01 · wma11 jan20 · IAS Maths Pure Mathematics 1 January 2020 · question 9.
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