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Applications of Differentiation - Stationary Points and Their Nature

Applications of Differentiation - Stationary Points and Their Nature

TGM Original Questions

A curve has the equation \(y = 12x^3 + 3x^2 - 6x + 1\).

  1. Find the coordinates of the stationary point(s) on the curve.
  2. Determine the nature of the stationary point(s) by using the first derivative test.
  3. Hence sketch the curve.

Solution:

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Answer:(i) \(\left(-\dfrac12,\dfrac{13}{4}\right)\), \(\left(\dfrac13,-\dfrac29\right)\) (ii) Maximum at \(\left(-\dfrac12,\dfrac{13}{4}\right)\); minimum at \(\left(\dfrac13,-\dfrac29\right)\)

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