Concept explainers
To determine how far did the flea jump and the maximum height of the jump.
The flea jumped for a distance of
Given:
Given the equation modelling the jump of the flea:
Concept Used:
Second derivative test:
Given a real valued function
The function will have a maximum at
The function will have a minimum at
The test fails when
Calculation:
Determine the distance up to which the flea jumped:
Since
Also, the distance of the jump is the value of
That is, the distance of the jump is value of
Substitute
Now,
But, the flea must have jumped for some distance.
That is,
Then, it follows that
That is, the flea jumped for a distance of
Find the maximum height of the jump:
Find the first derivative
Equate
Thus, it is found that
Now, find the second derivative
That is, the second derivative is negative everywhere.
In particular the second derivative
Then, by the second derivative test,
Find the value of
Thus, the maximum value of
That is, the maximum height of the jump is about:
Conclusion:
The flea jumped for a distance of
Chapter 1 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education