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Concept explainers
In Exercises 1–8, find all the relative and absolute extrema of the given function on the given domain (if supplied) or on the largest possible domain (if no domain is supplied).
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To calculate: The exact location of the relative and absolute extrema of the function
Answer to Problem 1RE
Solution:
The exact location of Absolute Minimum are
Explanation of Solution
Given Information:
The provided equation is:
Formula used:
First Derivative Test is, assume that for a critical point
If
If
If
Stationary Points are the points in the interior of the domain where the derivative is zero.
Singular Points are the points in the interior of the domain where the derivative is not defined.
Closed intervals contain end points which are the end points of the functions and the function does not have end points if the interval is open as open intervals do not have any end points.
Calculation:
Consider the provided equation:
Differentiate both sides of the equation with respect to
Now, locate stationary points.
Recall that stationary Points are the points in the interior of the domain where the derivative is zero.
Adding
Multiplying both sides of the equation by
Taking square root of both sides of the equation to get:
The domain of the function is
Now locate singular points.
Since
Next locate end points.
Since
The values of
5 | 5 |
The graph increases from
Use the above points to plot a graph
From figure we can see that
Classification | ||
Absolute Minimum | ||
Absolute Minimum | ||
Relative Maximum |
Therefore, the exact location of Absolute Minimum are
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