3 6 Critical Points Extrema Vocabulary Critical Points

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 f(a – h) > f(a) f(a + h) < f(a) Point of Inflection f(a – h) < f(a) f(a + h) > f(a) Pictures will be drawn on the board

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