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WMA11/01 Jan 2019, Question 6: Differentiating Roots and Fractional Powers

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 7 marks

The question, in short

For f(x) = 2x^(5/2) − 40x + 8 with x > 0, use calculus methods to solve two equations involving the first and second derivatives.

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Part (a) · 4 marks

Differentiate f(x) and solve f′(x) = 0 for x, giving an exact answer.

  1. 1f′(x) = 5x^(3/2) − 40
  2. 25x^(3/2) − 40 = 0 so x^(3/2) = 8
  3. 3x = 8^(2/3) = 4

Answerx = 4

Part (b) · 3 marks

Find the second derivative of f(x) and solve f″(x) = 5 for x.

  1. 1f″(x) = (15/2)x^(1/2)
  2. 2(15/2)x^(1/2) = 5 so x^(1/2) = 2/3
  3. 3x = 4/9

Answerx = 4/9

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