The correct choice from the given options.
Answer to Problem 2QQ
It has been determined that the given function has a
Explanation of Solution
Given:
The function,
Concept used:
The critical points of a function
If
The local minima (or maxima) where the function attains the least (or greatest) value is called the absolute minima (or maxima) of the function.
Calculation:
The given function is
Differentiating,
Simplifying,
On further simplification,
Finally,
Equating the first derivative of the function to obtain critical points,
This implies that the critical points are
Now, let
It follows that,
Then,
Similarly, let
It follows that,
Then,
Finally, let
It follows that,
Then,
So, it can be seen that
This implies that the given function has a relative maximum at
It can also be seen that
This implies that the given function has a relative minimum at
Thus, the given function has a relative maximum at
Conclusion:
It has been determined that the given function has a relative maximum at
Chapter 4 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning