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 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

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