a
To write the area as a function of x and the domain of the respective function.
a
Answer to Problem 13RE
Explanation of Solution
Given:
Equation is
Calculation:
The given equation can be alternatively written as :
From above equation, the co-ordinate ( x , y ) can be written as
From the graph, considering the above condition the area of the rectangle can be written as:
Now, the domain of the given function is the values of x for which the area of rectangle is defined.
Here, the area of rectangle is bounded in the region [0, 8].
Conclusion:
Hence, Area in terms of x will be:
b
To graph the function:
b
Answer to Problem 13RE
At x = 4 and y = 2 the area of the rectangle will be maximum.
Explanation of Solution
Given:
Graph:
By using graphing utility, the graph of area function is,
Interpretation:
From the above graph, it is clear that the maximum area will be 8 at x = 4.
Now, at x = 4,
Conclusion:
Hence, the required dimensions are
c
To solve the function algebraically and verify the answer with the graphical results.
c
Explanation of Solution
Given:
Calculation:
Now, in order to maximize the area
Hence, At x = 4, the area of the rectangle is maximum,
Verification with graph:
Interpretation:
The graph clearly states that at x = 4 the area of the rectangle will be maximum and it is equal to 8 sq. units.
Chapter 2 Solutions
Precalculus with Limits: A Graphing Approach
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