Two stationary points of different kinds

Two stationary points of different kinds

Secondary 4
7 marks
TGM Original Questions

A curve has equation \(y=\frac34x^4-2x^3+2\).

  1. Find and factorise \(\frac{\mathrm{d}y}{\mathrm{d}x}\).[2]
  2. Find the coordinates of both stationary points and determine the nature of each, giving reasons.[5]

Solution:

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Answer:(a) \(3x^2(x-2)\). (b) \((0,2)\): stationary inflexion; \((2,-2)\): minimum.

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