UNIT 3 — MILESTONE
3
SCORE
25/29
25/29 that's 86% RETAKE
25 questions were answered correctly. 4
questions were answered incorrectly.
1
The cost function, , in dollars for producing x
units is given by .
Approximate the cost of producing the 24th unit
by using the marginal cost.
$33.16
$32.82
$1347.90
$1314.90
RATIONALE
The marginal cost is the derivative of cost:
,The approximate cost of producing the 24th
unit is at . Evaluate :
Simplify:
CONCEPT
Applications of Rates of Change
Report an issue with this question
2
Use the limit definition of the derivative to find
when .
RATIONALE
The limit definition of the derivative is
, .
First, compute :
Then, replace with
and with :
Combine like terms in the numerator:
Separate the fractions:
Remove the common factor of “h” in
each fraction:
Evaluate the limit as h approaches 0 by
substituting 0 for h:
Thus, if , then .
CONCEPT
Definition of Derivative
Report an issue with this question
, 3
A square is to be designed with sides of
length 32 cm.
Use differentials to estimate the maximum error
when measuring the area of the square if the
possible error in measuring the side is 0.35
cm.
RATIONALE
The area of a square is , which has
the derivative .
Thus, the differential is .
Now, let and . Then, the
maximum error in estimating the area when
and
is:
3
SCORE
25/29
25/29 that's 86% RETAKE
25 questions were answered correctly. 4
questions were answered incorrectly.
1
The cost function, , in dollars for producing x
units is given by .
Approximate the cost of producing the 24th unit
by using the marginal cost.
$33.16
$32.82
$1347.90
$1314.90
RATIONALE
The marginal cost is the derivative of cost:
,The approximate cost of producing the 24th
unit is at . Evaluate :
Simplify:
CONCEPT
Applications of Rates of Change
Report an issue with this question
2
Use the limit definition of the derivative to find
when .
RATIONALE
The limit definition of the derivative is
, .
First, compute :
Then, replace with
and with :
Combine like terms in the numerator:
Separate the fractions:
Remove the common factor of “h” in
each fraction:
Evaluate the limit as h approaches 0 by
substituting 0 for h:
Thus, if , then .
CONCEPT
Definition of Derivative
Report an issue with this question
, 3
A square is to be designed with sides of
length 32 cm.
Use differentials to estimate the maximum error
when measuring the area of the square if the
possible error in measuring the side is 0.35
cm.
RATIONALE
The area of a square is , which has
the derivative .
Thus, the differential is .
Now, let and . Then, the
maximum error in estimating the area when
and
is:
