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Types of Stationary Points

2.2 Geometrical Application of Calculus. Types of Stationary Points. 1. Minimum. -. +. -. +. -. +. -. +. -. +. -. -. +. +. 0. 2.2 Geometrical Application of Calculus. Types of Stationary Points. 2. Maximum. -. 0. +. -. +. -. +. -. -. +. -. +.

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Types of Stationary Points

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  1. 2.2 Geometrical Application of Calculus Types of Stationary Points 1. Minimum - + - + - + - + - + - - + + 0

  2. 2.2 Geometrical Application of Calculus Types of Stationary Points 2. Maximum - 0 + - + - + - - + - +

  3. 2.2 Geometrical Application of Calculus Types of Stationary Points - + 3.Point of Horizontal Inflection - + - + - - + - + 0 - 0 - + - + - - +

  4. 2.2 Geometrical Application of Calculus Types of Stationary Points • Find any stationary points on the curve • f(x)=x2 - 2x & determine what type it is. f’(x)=2x - 2 f(1) = (1)2 – 2(1) = -1 Stationary @ (1, -1) 2x - 2 = 0 (Stationary) 2x = 2 f’(0)=2(0) - 2 = -2 x = 1 f’(2)=2(2) - 2 = +2 (1, -1) is a Minimum

  5. 2.2 Geometrical Application of Calculus Types of Stationary Points 2. Find the turning point on the curve y=2x3 + 2 and determine what type it is. f(x)=2x3 + 2 f(0) = 2(0)3 + 2 = 2 Stationary @ (0, 2) f’(x)=6x2 f’(-1)=6(-1)2 = +6 6x2 = 0 (Stationary) f’(1)=6(1)2 = +6 x = 0 (0, 2) is a horizontal point of inflection

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