
(a)
Whether h is a twice-differentiable function of x.
(a)

Answer to Problem 75E
The statement is true.
Explanation of Solution
Given information:
Where,
f has a negative derivative for all values of x and that
According to FTC (Fundamental Theorem of Calculus),
Then
Taking derivative again
According to the statement,
f has negative derivative for all values of x.
That means
Then
Therefore,
h is a twice differentiable function of x.
(b)
Whether h and
(b)

Answer to Problem 75E
The statement is true.
Explanation of Solution
Given information:
Where,
f has a negative derivative for all values of x and that
According to FTC (Fundamental Theorem of Calculus),
Then
Taking derivative again
Thus,
We have
Both
Therefore,
They both are continuous.
(c)
Whether the graph of h has a horizontal tangent at
(c)

Answer to Problem 75E
The statement is true.
Explanation of Solution
Given information:
Where,
f has a negative derivative for all values of x and that
If
h has a horizontal tangent at
Since
Then
According to the statement,
Therefore,
(d)
Whether h has
(d)

Answer to Problem 75E
The statement is true by the Second Derivative Test.
Explanation of Solution
Given information:
Where,
f has a negative derivative for all values of x and that
If
And
Then
h has a local maximum at
According to Part (c) result,
We have
Since
Then
According to the statement,
f has negative derivative for all values of x.
That means
Therefore,
(e)
Whether h has
(e)

Answer to Problem 75E
The statement is false by the Second Derivative Test.
Explanation of Solution
Given information:
Where,
f has a negative derivative for all values of x and that
If
And
Then
h has a local minimum at
According to Part (a) result,
We have
And
Then
And
According to statement,
Thus,
We also have
Thus,
Therefore,
h does not have a local minimum at
(f)
Whether the graph of h has an inflection point at
(f)

Answer to Problem 75E
The statement is false.
Explanation of Solution
Given information:
Where,
f has a negative derivative for all values of x and that
If
Then
h has an inflection point at
According to Part (a) result,
We have
And
Then
And
We also have
Thus,
Therefore,
h does not have an inflection point at
(g)
Whether the graph
(g)

Answer to Problem 75E
The statement is true.
Explanation of Solution
Given information:
Where,
f has a negative derivative for all values of x and that
We have
According to the statement,
f is a decreasing function.
That includes
Point (1, 0) because
Then
Therefore,
Chapter 6 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
Additional Math Textbook Solutions
Thinking Mathematically (6th Edition)
Calculus: Early Transcendentals (2nd Edition)
Calculus: Early Transcendentals (2nd Edition)
College Algebra (7th Edition)
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