Concept explainers
(a)
Whether g is differentiable function of x .
(a)
Answer to Problem 46RE
The statement is True.
Explanation of Solution
Given information:
Such that
g is differentiable function if g’ is continuous.
Since
Then
According the statement,
Thus,
Since
Then
Therefore,
g is a differentiable function of x .
(b)
Whether g is a continuous function of x
(b)
Answer to Problem 46RE
The statement is True.
Explanation of Solution
Given information:
Such that
Since
Then
According the statement,
Thus,
Since
Then
We have already discussed in Part (a),
g is differentiable function if g’ is continuous.
Therefore,
g is a continuous function of x .
(c)
Whether the graph of g has a horizontal tangent line at
(c)
Answer to Problem 46RE
The statement is True.
Explanation of Solution
Given information:
Such that
Since
Then
According the statement,
Then
Therefore,
The graph of g has a horizontal tangent line at
(d)
Whether g has a
(d)
Answer to Problem 46RE
The statement is False.
Explanation of Solution
Given information:
Such that
If
Then
By the Second Derivative Test:
And
Since
Then
According the statement,
Then
We also have
Such that
Therefore,
(e)
Whether g has a
(e)
Answer to Problem 46RE
The statement is True.
Explanation of Solution
Given information:
Such that
If
Then
By the Second Derivative Test:
And
Since
Then
According the statement,
Then
We also have
Such that
Thus,
Therefore,
(f)
Whether the graph of g has an infection point at
(f)
Answer to Problem 46RE
The statement is False.
Explanation of Solution
Given information:
Such that
If
Then
However,
Such that
Thus,
(g)
Whether the graph of
(g)
Answer to Problem 46RE
The statement is True.
Explanation of Solution
Given information:
Such that
Since
And
Then
Since
Then
Such that
Instead of the alternative of bouncing − off of the x − axis at (1, 0),
Therefore,
Chapter 6 Solutions
Calculus: Graphical, Numerical, Algebraic
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