The local extreme values and any absolute extremum of the given function.
Answer to Problem 3E
It has been determined that
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,
Equating the first derivative to zero to obtain the critical points,
Solving,
So, the critical points of the given function are
Let
It follows that,
Then,
Similarly, let
It follows that,
Then,
Similarly, let
It follows that,
Then,
Finally, let
It follows that,
Then,
So,
So,
So,
Put
It should be noted that
This implies that the given function is decreasing for
So,
However, the given function does not contain any absolute maximum value.
Conclusion:
It has been determined that
Chapter 4 Solutions
CALCULUS-W/XL ACCESS
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