The lengths of pregnancies are normally distributed with mean µ = .docx

The lengths of pregnancies are normally distributed with mean
µ = 268 days and standard deviation σ = 15 days.
25. (a) If one pregnant woman is chosen at random, find the
probability that her length of pregnancy is between 260 and 278
days.
(b) Find the number of days above which lie the longest 1.5% of
all pregnancies.
9/16/2016 xyzHomework Assessment
http://www.xyzhomework.com/imathas/assessment/printtest.php
1/3
Name: Ian Tapia2.5
#1 Points possible: 1. Total attempts: 3
Find for the function.
The number
(in thousands) of cat flea collars demanded each year when the
price of a collar is dollars is
expressed by the function
. The collars are currently selling for each and the annual
number of sales is
. Find the approximate decrease in sales of the collar if the pric

e of each collar is
raised by .
The approximate decrease in sales is about collars.
The monthly revenue
(in dollars) of a telephone polling service is related to the num
ber of completed
responses by the function
If the number of completed responses is increasing at the rate of
forms per month, find the rate at which
the monthly revenue is changing when .
The monthly revenue is changing by .
y'
2y3 − x4 = − 8
y' =
x p
x
3 + 250p2 = 15, 500 $4
22, 572

$1
y'
3√(y − 1)2 = − 2 + 3x
y' =
R x
R(x) = − 13000 + 15√4x2 + 20x 0 ≤ x ≤ 1000
10
x = 500
$
2/3
Find for at the point .
At ,
At ,

At ,
The cost (in dollars) of manufacturing
number of high-quality computer laser printers is
Currently, the level of production is
printers and that level is increasing at the rate of printers per
month. Find the rate at which the cost is increasing each month.
The cost is increasing at about per month.
y' 3x5 + 2y4 − 3 = 26 ( − 1, − 2)
( − 1, − 2) y' =
y' (xy)3 / 2 = 64 (8, 2)
(8, 2) y' =
y' x − 3 + y − 3 = −
7
8
(2, − 1)
(2, − 1) y' =
C x
C(x) = 18x4 / 3 + 12x2 / 3 + 400, 000

729 400
$
3/3
For the circle ,
find when .
find the slope of the tangent line where .
The slope of the tangent line at is .
find the points at which .
at
If the radius starts increasing at a constant rate of
cm/sec, how fast is the area increasing when
cm?
The area is increasing at square cm per second.

At ,
x
2 + y2 = 25
a. y x = 4
y =
b. x = 4
x = 4
c. = 0
dy
dx
= 0
dy
dx
d. 3 r = 9
y'
(y − 1)4 = 3x2 − 5x − 1
y' =
y' x2y2 + 2x − y = 1 ( − 2, − 1)
( − 2, − 1) y' =

1/4
Name: Ian Tapia2.4
Find the derivative of the function
at .
Find
without using the quotient rule; rather, rewrite the function by
using a negative exponent and then
use the product rule and the general power rule to find the deriv
ative.
If and , find and .
Find , if

and .
f(x) = (x2 − 3)
3
(3x − 5)4 x = 2
f' (2) =
dy
dx
y =
1
x + 5
=
dy
dx
f(x) = x2 g(x) = 3x3 − 3x + 5 (f ∘ g)(x) (g ∘ f)(x)
a. (f ∘ g)(x) =
b. (g ∘ f)(x) =
dy
dx
y = u3 − 2u u = 3x2 + 3
=

dy
dx
2/4
Find
ative.
If and , find .
Find , if
.
Find , if

and .
at .
dy
dx
y = ( )
42x + 3
4x + 5
=
dy
dx
u(x) = 4x2 − 5 v(x) = x3 − 6 u(x) ⋅ v(x)
u(x) ⋅ v(x) =
dy
dx
y = (4x2 + 5x + 3)
3

=
dy
dx
dy
dx
y = 3u2 + 3u − 2 u = 6x + 2
=
dy
dx
f(x) = (4x2 + 3x − 5)
3
x = 1
f' (1) =
3/4
Find

ative.
Find , if
.
at .
Find , if
and .
dy
dx
y =
(x2 − 3)
3
x + 3

=
dy
dx
dy
dx
y = 5√(x2 + 7)3
=
dy
dx
f(x) = 3√(x2 − 2)2 x = 1
f' (1) =
dy
dx
y = 7u − 3 u = 5x + 9
=
dy
dx

4/4
Find , if
and .
Find , if
.
dy
dx
y = 3u + 4 u = − 2x2 − 2
=
dy
dx
dy
dx
y = (x2 + 1)
3
(3x + 3)4
=

dy
dx
1/4
Name: Ian Tapia2.3
Suppose
represents the amount of money (in thousands of dollars) a cou
ntry spends on the local drug
war months from January ,
. Interpret the information provided by and .
Because the derivative of is Select an answer
, the cost of the drug war is Select an answer . Because
the second derivative is Select an answer
(so that the derivatives have Select an answer ), the function
is Select an answer and the function is Select an answer
at a(n) Select an answer rate.
Find and
3/16

‑3/32
Find , , and for the function.
6x^5‑10x^4+4
30x^4‑40x^3
120x^3‑120x^2
360x^2‑240x
C(t)
t 1 2000 C' (14) = 2.3 C' ' (14) > 0
C
C' (t) C(t)
f' (x) f' ' (x)
f(x) =
4x − 3
x
f' (x) =
f' ' (x) =
f' f' ' f' ' ' f ( 4 )
f(x) = x6 − 2x5 + 4x − 4

f' (x) =
f' ' (x) =
f' ' ' (x) =
f
( 4 ) (x) =
2/4
Find , , and for the function.
Find and interpret and .
3/2
3/2
So at , is decreasing at a(n) decreasing rate.

3/8
‑2/27
So at , is decreasing at a(n) increasing rate.
f' f' ' f' ' ' f ( 4 )
f(x) = x4 − x3 + 10x − 1
f' (x) =
f' ' (x) =
f' ' ' (x) =
f
( 4 ) (x) =
f' (4) f' ' (4)
f(x) = 6√x
f' (4) =
f' ' (4) =
x = 4 f(x)
f' (27) f' ' (27)
f(x) = 9 3√x
f' (27) =

f' ' (27) =
x = 27 f(x)
3/4
9
‑2
So at , is increasing at a(n) increasing rate.
Find and
5‑4/x^3
12/x^4
If , then

The values of for which are ,
The values of for which are
f' ( − 2) f' ' ( − 2)
f(x) = − x2 + 5x + 4
f' ( − 2) =
f' ' ( − 2) =
x = − 2 f(x)
f' (x) f' ' (x)
f(x) =
5x3 + 2
x2
f' (x) =
f' ' (x) =
f(x) = (4x + 1)(2x − 1)
a. f(1) =
b. f' (1) =
c. f' ' (1) =
d. x f(x) = 0

e. x f' (x) = 0
4/4
Find , , and
for the function. You will answer the coefficient in the first bo
x and then select
the term for each.
Select an answer
Select an answer
Select an answer
Select an answer
So at , is Select an answer at a(n) Select an answer rate.

So at , is Select an answer at a(n) Select an answer rate.
f' f' ' f' ' ' f ( 4 )
x
f(x) = − 12√x
f' (x) =
f' ' (x) =
f' ' ' (x) =
f
( 4 ) (x) =
f' (1) f' ' (1)
f(x) =
2
x
f' (1) =
f' ' (1) =
x = 1 f(x)
f' (1) f' ' (1)
f(x) = 9x
4
3

f' (1) =
f' ' (1) =
x = 1 f(x)

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