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TMUA 2022 · Paper 2 · Question 1 of 20

TMUA 2022 Paper 2 Question 1

Differentiation and integration — Stationary points of a quartic. Try it first; the answer and a full worked solution are below.

TMUA 2022 · Paper 2Differentiation and integrationStationary points of a quartic5 options
Determine the number of stationary points on the curve with equation y = 3x4 + 4x3 + 6x2 − 5
  1. A0
  2. B1
  3. C2
  4. D3
  5. E4
Show the answer and worked solution
answer · B
  1. A0
  2. B1
  3. C2
  4. D3
  5. E4
Differentiating, dydx = 12x3 + 12x2 + 12x = 12x(x2 + x + 1). The quadratic factor has discriminant 1 − 4 = −3 < 0, so it never vanishes. Only x = 0 makes the derivative zero, giving one stationary point.