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TMUA 2018 · Paper 2 · Question 1 of 20

TMUA 2018 Paper 2 Question 1

Differentiation and integration — Differentiating after splitting a quotient into powers. Try it first; the answer and a full worked solution are below.

TMUA 2018 · Paper 2Differentiation and integrationDifferentiating after splitting a quotient into powers6 options
The function f is given, for x > 0, by f(x) = x3 − 4x2√x Find the value of f'(4).
  1. A3
  2. B9
  3. C9.5
  4. D12
  5. E39.5
  6. F88
Show the answer and worked solution
answer · C
  1. A3
  2. B9
  3. C9.5
  4. D12
  5. E39.5
  6. F88
Do not reach for the quotient rule. Split the fraction first and write everything as a power of x: f(x) = 12x3x−1/2 − 2x x−1/2 = 12x5/2 − 2x1/2. Differentiating, f'(x) = 54x3/2 − x−1/2. At x = 4 this is 54× 8 − 12 = 10 − 0.5 = 9.5.