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LCHL Strand 5 Functions/Calculus Stationary Points

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Presentation on theme: "LCHL Strand 5 Functions/Calculus Stationary Points"— Presentation transcript:

1 LCHL Strand 5 Functions/Calculus Stationary Points
Turning Points, Points of Inflection, Horizontal Points of Inflection Culan O’Meara – Ballinrobe Community School

2 Stationary Points Three types: Turning points Inflection Points
Horizontal Inflection Points Author: Culan O'Meara

3 Turning Points Can either be local maximum or minimum points of function f(x) At both points, slope of f = 0 [f’(x) = 0] Author: Culan O'Meara

4 Turning Points Local Maximum = Point where slope goes from positive to negative Author: Culan O'Meara

5 Turning Points Local Maximum = Point where slope goes from positive to negative Author: Culan O'Meara

6 Turning Points Local Minimum = Point where slope goes from negative to positive Author: Culan O'Meara

7 Turning Points Local Minimum = Point where slope goes from negative to positive Author: Culan O'Meara

8 Turning Points Local Minimum = Point where slope goes from negative to positive Author: Culan O'Meara

9 Turning Points On this graph there are no turning points but it does have an inflection point Author: Culan O'Meara

10 Inflection Points Point where slope of curve goes from increasing in steepness to decreasing (or vice versa) Author: Culan O'Meara

11 Inflection Points Point where Slope of f’(x) =0 [f’’(x)=0]
Author: Culan O'Meara

12 Horizontal Inflection Points
Special case where the point is both a stationary point and an inflection point Two conditions must be met: f’(x)=0 f’’(x)=0 Author: Culan O'Meara

13 Horizontal Inflection Points
There are none on the graph we have been using as at no point is f’(x) = f’’(x)=0 Author: Culan O'Meara

14 Horizontal Inflection Points
On this graph, both f’(x) and f’’(x) = 0 at x = 0 Author: Culan O'Meara

15 Turning Points From earlier, this graph, this point can’t be a horizontal inflection point because it doesn’t meet the two conditions outlined Author: Culan O'Meara

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