3.6A Summary of Curve Sketching

Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 1995

Old Faithful Geyser, Yellowstone National Park

3.6A Summary of Curve Sketching

Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2007

Yellowstone Falls, Yellowstone National Park

3.6A Summary of Curve Sketching

Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2007

Mammoth Hot Springs, Yellowstone National Park

Objective

• Analyze and sketch the graph of a function.

In the past, one of the important uses of derivatives was as an aid in curve sketching. Even though we usually use a calculator or computer to draw complicated graphs, it is still important to understand the relationships between derivatives and graphs.

First derivative:

y is positive Curve is increasing.

y is negative Curve is decreasing.

y is zero Possible local maximum or minimum.

Second derivative:

y is positive Curve is concave up.

y is negative Curve is concave down.

y is zero Possible inflection point(where concavity changes).

Analyze the graph of 2

2

2( 9)( )

4

x

f xx

Analyze the graph of 2

2

2( 9)( )

4

x

f xx

Homework

3.6 (page 208)

#1-5 all

#7 and 9