a.
Find the values at which the absolute maximum of
a.
Answer to Problem 28E
The absolute
Explanation of Solution
Given:
The function
Concept Used:
Calculation:
Function:
Differentiate the
For absolute maxima put
So, absolute maxima of function
Conclusion:
The absolute maxima of function
b.
Complete the table.
b.
Answer to Problem 28E
0.1 | 3.7150 | |
0.2 | 2.8650 | 0.4356 |
0.3 | 2.3646 | 0.4589 |
0.4 | 2.0188 | 0.4341 |
0.5 | 1.7564 | 0.3809 |
0.6 | 1.5474 | 0.3118 |
0.7 | 1.3755 | 0.2346 |
0.8 | 1.2308 | 0.1549 |
0.9 | 1.1071 | 0.0757 |
1 | 1 | 0 |
Explanation of Solution
Given:
The function
Graph of function
Calculation:
According to graph,
Then,
So, the graph is
Area of rectangle
Area of rectangle is
Similarly, find the other values. The table is
0.1 | 3.7150 | |
0.2 | 2.8650 | 0.4356 |
0.3 | 2.3646 | 0.4589 |
0.4 | 2.0188 | 0.4341 |
0.5 | 1.7564 | 0.3809 |
0.6 | 1.5474 | 0.3118 |
0.7 | 1.3755 | 0.2346 |
0.8 | 1.2308 | 0.1549 |
0.9 | 1.1071 | 0.0757 |
1 | 1 | 0 |
c.
To Draw: a
c.
Answer to Problem 28E
Explanation of Solution
Given:
0.1 | 3.7150 | |
0.2 | 2.8650 | 0.4356 |
0.3 | 2.3646 | 0.4589 |
0.4 | 2.0188 | 0.4341 |
0.5 | 1.7564 | 0.3809 |
0.6 | 1.5474 | 0.3118 |
0.7 | 1.3755 | 0.2346 |
0.8 | 1.2308 | 0.1549 |
0.9 | 1.1071 | 0.0757 |
1 | 1 | 0 |
Calculation:
Here,
d.
To Find the quadratic, cubic and quartic regression equations for the data in part (b).
d.
Answer to Problem 28E
The absolute maxima of function
Explanation of Solution
Given:
The table is
0.1 | |
0.2 | 0.4356 |
0.3 | 0.4589 |
0.4 | 0.4341 |
0.5 | 0.3809 |
0.6 | 0.3118 |
0.7 | 0.2346 |
0.8 | 0.1549 |
0.9 | 0.0757 |
1 | 0 |
Concept used:
Quadratic regression equation:
Here,
Calculation:
Quadratic regression equation:-
Here,
On solving,
Similarly, find the cubic and quartic regression equations.
Cubic regression equations
Quartic regression equations
Conclusion:
Quadratic regression equation
Cubic regression equations
Quartic regression equations
d.
Find maximum possible value of the area using the regression equations.
d.
Answer to Problem 28E
From quadratic regression equation,
Maximum possible area of the rectangle is
From cubic regression equation,
Maximum possible area of the rectangle is
From quartic regression equation,
Maximum possible area of the rectangle is
Explanation of Solution
Given:
Quadratic regression equation
Cubic regression equations
Quartic regression equations
Calculation:
Draw the graphs of regression equations,
Now, according to graph,
From quadratic regression equation,
Maximum possible area of the rectangle is
From cubic regression equation,
Maximum possible area of the rectangle is
From quartic regression equation,
Maximum possible area of the rectangle is
Conclusion:
For quadratic regression equation:
For cubic regression equation:
For quartic regression equation:
Chapter 4 Solutions
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