3.6 – Critical Points & Extrema

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

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

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

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

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

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

Testing for Critical Points let x = a be the critical point for f(x) h is a small value greater than zero Maximum f(a – h) < f(a) f(a + h) < f(a) Minimum f(a – h) > f(a) f(a + h) > f(a) Point of Inflection Pictures will be drawn on the board

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