Math 121

Section 3.2

Extrema Points

Absolute Minimum Absolute Maximum

Relative Minimum and Relative Maximum

Inflection Point

Types of Critical Points

1) Relative Maximum

2) Relative Minimum

3) Absolute Maximum

4) Absolute Minimum

Testing for Extrema Points

Find all an extrema points of the function.

1)

Interval
Test Value	x = -1	x = 1
Sign of	Negative	Positive
Conclusion	Decreasing	Increasing

The function is increasing when x is less than -1 and increasing when x is greater than -1.

2) Find all extrema points of the function.

Interval
Test Value	x = -1	x = 1
Sign of	Positive	Positive
Conclusion	Increasing	Increasing

The function is increasing when x is less than zero and greater than zero, so the function has an inflection point at x = 0. (See graph above)

3) Find all extrema points of the function.

Interval
Test Value	x = -1	x =	x = 2
Sign of	Positive	Negative	Positive
Conclusion	Increasing	Decreasing	Increasing

The function has a relative maximum at x = 0 and a relative minimum at x = 1

(See diagram above)

4)

Interval
Test Value	x = -1	x = 1
Sign of	Positive	Negative
Conclusion	Increasing	Decreasing

The function has an absolute maximum at x = 0

See Graph