a.
To calculate: The derivatives of the function.
a.
Answer to Problem 47E
The derivatives of all the three functions is
Explanation of Solution
Given information:
The functions are
Concept used:
The slope of a function is the derivative of the function.
Calculation:
The function is
Differentiate the equation of curve
The function is
Differentiate the equation of curve
The function is
Differentiate the equation of curve
Conclusion: So, the derivatives of all the three functions are
b.
To graph: the derivatives of the functions.
b.
Answer to Problem 47E
The graph of the all the three derivatives have been plotted.
Explanation of Solution
Given information:
The functions are
Calculation:
The derivatives of all the three functions are
Graph of all the derivates in one graph is shown below.
Conclusion: So, the graph has been plotted.
c.
To calculate: The family of function.
c.
Answer to Problem 47E
The family is
Explanation of Solution
Given information:
The functions are
Concept used:
The formula is
Calculation:
The differentiation of
Conclusion: So, the family of functions is
c.
To calculate: The family of function.
c.
Answer to Problem 47E
The family is
Explanation of Solution
Concept used:
The formula is
Given information:
The functions are
Concept used:
The formula is
Calculation:
The differentiation of
Conclusion: So, the family of functions is
d.
To calculate: The function following the properties.
d.
Answer to Problem 47E
The function is
Explanation of Solution
Given information:
The functions are
Concept used:
The formula is
Calculation:
The differentiation of
The function
Conclusion: So, the function is
e.
To find: the function which satisfy the given properties.
e.
Answer to Problem 47E
Yes, the function is
Explanation of Solution
Given information:
The derivative of functions
Concept used:
The formula is
Calculation:
The differentiation of
The function
Conclusion: So, the function is
Chapter 2 Solutions
AP CALCULUS TEST PREP-WORKBOOK
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