Question
The marketing research department of a computer company used a large city to test market the firm’s new laptop. The department found the relationship between price
if necessary, fill in the answer box to complete your choice.
A. The graph is concave upward on
(Type your answer in interval notation.)
B. The graph is never concave upward.
On which intervals is the graph of the revenue function concave downward? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The graph is concave downward on
(Type your answer in interval notation.)
B. The graph is never concave downward.
if necessary, fill in the answer box to complete your choice.
A. The graph is concave upward on
(Type your answer in interval notation.)
B. The graph is never concave upward.
A. The graph is concave downward on
(Type your answer in interval notation.)
B. The graph is never concave downward.
Upstudy AI Solution
Tutor-Verified Answer
Answer
- The graph is never concave upward.
- The graph is concave downward on
.
Solution
We start with the revenue function
- Compute the first derivative:
- Compute the second derivative:
- Analyze the concavity:
-
The graph is concave upward when
. Since and the domain is, there are no values of in the interval for which . Thus, the graph is never concave upward. -
The graph is concave downward when
. Since the graph is concave downward on the entire domain.
-
Therefore,
- For concave upward, the answer is: B. The graph is never concave upward.
- For concave downward, the answer is: A. The graph is concave downward on
.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Explain 
Simplify this solution Mind Expander
To determine the concavity of the revenue function
The first derivative is:
The second derivative is:
Now, let’s analyze the second derivative,
A. The graph is concave upward on
B. The graph is never concave upward.
As for concavity downward, since
A. The graph is concave downward on
B. The graph is never concave downward is incorrect.
