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Understanding Critical Points and Extrema in Graphs

Learn about critical points, maximum, minimum, inflection points, and extrema in graph analysis. Explore examples and practice drawing tangent lines. Enhance your graph analysis skills today!

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Understanding Critical Points and Extrema in Graphs

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  1. 3.6 – Critical Points & Extrema

  2. Vocabulary • Critical Points – points on a graph in which a line drawn tangent to the curve is horizontal or vertical • Maximum • Minimum • Point of Inflection

  3. Maximum • When the graph of a function is increasing to the left of x = c and decreasing to the right of x = c.

  4. Minimum • When the graph of a function is decreasing to the left of x = c and increasing to the right of x = c

  5. Relative Extrema • A maximum/minimum of a function in a specific interval. • It is not necessarily the max/min for the entire function

  6. Absolute Extrema • Extrema – the general term of a maximum or minimum. • Absolute Extrema – the greatest/smallest value of a function over its whole domain

  7. Point of Inflection • Not a maximum or minimum • “Leveling-off Point” • When a tangent line is drawn here, it is vertical

  8. Testing for Critical Pointslet x = a be the critical point for f(x)h is a small value greater than zero Pictures will be drawn on the board

  9. Let’s Look at Page 176 # 4 – 5, 8 – 11 We will do these together as examples

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