C I need to put 20 letters so yea the answer is C
a. Note that
is continuous for all
. If
attains a maximum at
, then
. Compute the derivative of
.

Evaluate this at
and solve for
.




To ensure that a maximum is reached for this value of
, we need to check the sign of the second derivative at this critical point.

The second derivative at
is negative, which indicate the function is concave downward, which in turn means that
is indeed a (local) maximum.
b. When
, we have derivatives

Inflection points can occur where the second derivative vanishes.




Then we have three possible inflection points when
,
, or
.
To decide which are actually inflection points, check the sign of
in each of the intervals
,
,
, and
. It's enough to check the sign of any test value of
from each interval.




The sign of
changes to either side of
and
, but not
. This means only
and
are inflection points.
No because it does not pass the vertical line test,
meaning that a single vertical line could pass through multiple points on the graph.
The cost of the 15 percent of replaced vacuum cleaner which are sold under warranty is $3,681,384. Option b is correct.
<h3>What is percentage ?</h3>
Percentage of a number is the part of the number expressed in the in every hundred. Percentage of a number is expressed with the symbol '%'.
A vacuum cleaner costs $68, and the full-replacement extended warranty costs $22.
The manufacturer sells 360,920 vacuum cleaners under warranty and must replace 15% of them to honor the warranties. Thus, the number of vecuum cleaner replaced by manufacturer is,

The cost of one vacuum cleaner is $68. Thus the cost of 54138 vcacuum cleaner is,

Hence, the cost of the 15 percent of replaced vacuum cleaner which are sold under warranty is $3,681,384. Option b is correct.
Learn more about the percentage here;
brainly.com/question/24304697