3.3. The First Derivative Test http://www.ck12.org
We observe that the slopes of the tangent lines to the graph change from negative to positive atx=− 3 .The first
derivative test verifies this fact. Note that the slopes of the tangent lines to the graph are negative forx∈(−∞,− 3 )
and positive forx∈(− 3 ,−∞).
Lesson Summary
- We found intervals where a function is increasing and decreasing.
- We applied the First Derivative Test to find extrema and sketch graphs.
Multimedia Links
For more examples on determining whether a function is increasing or decreasing(9.0), see Math Video Tutorials
by James Sousa, Determining where a function is increasing and decreasing using the first derivative (10:05).
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/552For a video presentation of increasing and decreasing trigonometric functions and relative extrema(9.0), see Math
Video Tutorials by James Sousa, Increasing and decreasing trig functions, relative extrema (6:03).