Question
Summarize all pertinent information obtained by applying the graphing strategy and sketch the graph of
.
Find the intervals where
is concave upward or downward. Select the correct choice below and fill in the answer box(es) to complete your choice.
A. The function is concave upward on
(Type an exact answer. Type your answer in interval notation. Use a comma to separate answers as needed.)
B. The function is concave upward on
. It is concave downward on
(Type exact answers. Type your answers in interval notation. Use commas to separate answers as needed.)
C. The function is concave downward on
. It is never concave upward.
(Type an exact answer. Type your answer in interval notation. Use a comma to separate answers as needed.)
Find the location of any inflection points of
. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. There is an inflection point at
.
(Type an integer or a decimal. Use a comma to separate answers as needed.)
B. There are no inflection points.
Find the intervals where
A. The function is concave upward on
(Type an exact answer. Type your answer in interval notation. Use a comma to separate answers as needed.)
B. The function is concave upward on
C. The function is concave downward on
(Type an exact answer. Type your answer in interval notation. Use a comma to separate answers as needed.)
Find the location of any inflection points of
A. There is an inflection point at
(Type an integer or a decimal. Use a comma to separate answers as needed.)
B. There are no inflection points.
Ask by May Weber. in the United States
Mar 17,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The function
has no inflection points and is concave downward everywhere.
Solution

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Bonus Knowledge
To analyze the function
, we can start by simplifying it. The numerator can be factored to
, and the denominator is
. This indicates a removable discontinuity at
, where the function approaches a limit.
Next, we need to find the second derivative
to determine concavity. The first derivative can be obtained using the quotient rule, and once simplified, you can differentiate again. After analysis, you will find that
is concave upward on the interval
and concave downward on
.
Regarding inflection points, we analyze
and solve for when it equals zero. You will discover that the inflection point occurs at
.
Final Answers:
A. The function is concave upward on .
B. The function is concave upward on . It is concave downward on
.
A. There is an inflection point at .
A. The function is concave upward on
B. The function is concave upward on
A. There is an inflection point at