calc notes lecture 15

# calc notes lecture 15 - Example 2 Find all relative extrema...

This preview shows pages 1–7. Sign up to view the full content.

Lecture Section Objectives Assignment 15 3.2 Extrema and the First-Derivative Test 3.2: 1, 5-11 odd, 19-29 odd, 35, 39 Understanding Goals: 1. Understand the difference between relative extrema and absolute extrema. 2. Understand how to use the First-Derivative Test to find the relative extrema of functions. 3. Understand how to find absolute extrema of continuous functions on a closed interval. 4. Understand how to find minimum and maximum values of real-life models and interpret the results in context. A function has a relative extremum at points where the function changes from increasing to decreasing or vice versa. 1

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

View Full Document
For a continuous function, the relative extrema must occur at critical numbers of the function. 2
3

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

View Full Document
Example 1 : Find all relative extrema of the function 3 2 ( ) 2 3 36 14 f x x x x = - - + . Interval Test Value Sign of f '( x ) Conclusion

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

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

Unformatted text preview: Example 2 : Find all relative extrema of the function 2 3 ( ) 2 3 f x x x =-. 4 5 Example 3 : Find the minimum and maximum values of 2 2 ( ) 3 t g t t = + on the interval [ ] 1,1-. 6 Example 4 : Coughing force the trachea (windpipe) to contract, which affects the velocity v of the air passing through the trachea. The velocity of the air during coughing is 2 ( ) , v k R r r r R =-< where k is constant, R is the normal radius of the trachea, and r is the radius during coughing. What radius will produce the maximum air velocity? Example 5 : Poiseuille’s Law asserts that the speed of blood that is r centimeters from the central axis of an artery of radius R is ( 29 2 2 ( ) S r c R r =-, where c is a positive constant. Where is the speed of the blood greatest? 7...
View Full Document

{[ snackBarMessage ]}

### Page1 / 7

calc notes lecture 15 - Example 2 Find all relative extrema...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online