(a.)
Why the lowest point on the given graph must occur when
It has been explained why the lowest point on the given graph must occur when
Given:
The graph of
Concept used:
The least possible value of a square quantity is zero.
Calculation:
As discussed, the least possible value of a square quantity is zero.
Then,
Now, it is given that
Then,
Simplifying,
That is,
This implies that the lowest point on the given graph occurs when
Put
Simplifying,
On further simplifying, since
Solving,
Finally,
This explains why the lowest point on the given graph must occur when
Conclusion:
It has been explained why the lowest point on the given graph must occur when
(b.)
If the lowest point on the given graph occurs when
It has been determined that the reasoning from part (a) is not valid for the given graph and thus the lowest point on the given graph does not occur when
Given:
The graph of
Concept used:
There is no finite least possible value of a cubic quantity.
Calculation:
As discussed, there is no finite least possible value of a cubic quantity.
Then,
Now, it is given that
Then,
Simplifying,
That is,
This implies that there is no finite lowest point on the given graph.
So, the reasoning from part (a) is not valid for the given graph.
Conclusion:
It has been determined that the reasoning from part (a) is not valid for the given graph and thus the lowest point on the given graph does not occur when
Chapter 4 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
- 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