Concept explainers
To find: The
Answer to Problem 3RE
The
The absolute maximum occurs at
The absolute minimum is
Explanation of Solution
Given:
The function is,
Calculation:
Obtain the first derivative of the given function.
Set
Apply
Thus, the value of
Thus, the critical numbers are
Apply the extreme values of the given interval and the critical number
Substitute
Substitute
Substitute
Since the largest functional value is the absolute maximum and the smallest functional value is the absolute minimum, the absolute maximum of
Therefore, the absolute maximum of
To find the local maximum and minimum obtain the second derivative of the function.
Substitute the critical numbers in the second derivative and obtain the local maximum and minimum as follows.
Substitute
Thus, the local minimum occurs at
Chapter 4 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition