# Calc04_3 - 4.3 Using Derivatives for Curve Sketching Old...

• Notes
• 10

This preview shows pages 1–6. Sign up to view the full content.

4.3 Using Derivatives for Curve Sketching Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 1995 Old Faithful Geyser, Yellowstone National Park

This preview has intentionally blurred sections. Sign up to view the full version.

4.3 Using Derivatives for Curve Sketching Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 1995 Yellowstone Falls, Yellowstone National Park
In the past, one of the important uses of derivatives was as an aid in curve sketching. We usually use a calculator of computer to draw complicated graphs, it is still important to understand the relationships between derivatives and graphs.

This preview has intentionally blurred sections. Sign up to view the full version.

First derivative: y is positive Curve is rising. y is negative Curve is falling. 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).
Example: Graph ( 29 ( 29 2 3 2 3 4 1 2 y x x x x = - + = + - There are roots at and .

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern