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 Pointslet 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