# PPSU Critical Point & Relative Maximum or Relative Minimum Question

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Question 4 of 43
-/1
III
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Use the given derivative to find all critical points off and at each critical point determine whether a relative maximum, relative
minimum or neither occurs. Assume that f is continuous everywhere.
3 – 4x
f'(x) =
Vx+2
Enter the exact answers in increasing order.
• X=
.
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Q
N
Qu
Question 5 of 43

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9
VE
G
Use a graphing utility to estimate the absolute maximum and
minimum values of f, if any, on the stated interval, and then use
calculus methods to find the exact values.
14 – 7 cosa
f(x) =
sin
If there is no absolute maximum or minimum on the given interval,
indicate that using the check box.
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3
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View
Math
Graph
An absolute minimum value of
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occurs at
No absolute minimum
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An absolute maximum value of
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occurs at 2
No absolute maximum
Question
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Question 7 of 43
-11
Questi
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Multipart
Verify that the hypothesis of Mean-Value Theorem are satisfied on the given interval, and find a value of cin that interval that
satisfies the conclusion of the theorem.
f) = x + x2 on (-1.2)
Question
Math Symbol
Graphing
Question
Mutta
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Question 4
Numerical
Question 5
Math Symbol
Graphing
Question 6
Math Symboler
Graphic
Vieving Ques
Numerical
Question 8
Numeric Maple
Question 9
Math Symboland
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Question 8 of 43
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ini
Ques
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Let
Questic
Multipart
s(x) = { 18+
XSI
> 1
Questio
Graphing
Find the values of a and b so that will be differentiable at x = 1.
Question
Muitstep
a=
Question
Numer Map
be
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Math Symbol
Graphing
Question 6
Math Symbol
Graphing
Question 7
Numerie
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Numeri Maple
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Question 9 of 43

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Let g(x) = x3 – 2x + 4. Find f(x) so that f'(x) = f'(x) and f(1) = 1.
f(1) =
C
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Vies
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Question 10 of 43
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Que
Much
Grapt
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Ques
Maths
Graph
Use simple area formulas from geometry to find the area function
A(z) that gives the area between the graph of the function
f(x) = 232 – 23 and the interval [1, 2]. Confirm that A'(x) = f(x).
Questi
Numeric
Questio
Numeric
Question
Math Symbo
Graphing
A(2) =
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10
och Symbol
Graphing
Question 11
Symbok
Graphic
Question 12
Mach Symbocand
Graph
Question 13
Symbok and
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Question 15 of 43
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Express the sum
Σ
M
72
7k
3n
k=1
in closed form.
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15
M
Grap
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Ques
Numer
Questi
Numene
Questio
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Numer Ma
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Mathybo
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Question 17 of 43
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Find
(196) – slo)dirir
,
f(x)dx = 7 and
8(x)dx = 4
I.
13
[9f(x) – g(x)]dx =
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Question 20 of 43

-/1
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Use the following theorem to evaluate the given integrals.
Theorem: If f is integrable on a closed interval containing the
three points a, b, and, c then
[ f(z) dx = [“s(z) ds +
s() dx + [ f(a) der
N
no matter how the points are ordered.
O
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SERS
(a) 18+ fel der =
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(b) 1 1/2 – cos z do
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Question 21 of 43
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Find the average value of the function f(x) = 19 sin(x) over the
interval (0, 1)
fave
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Question 22 of 43
(1)
N
=
2
QL
M
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Que
Ques
Ques
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Question 39 of 43

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X
Incorrect.
Use implicit differentiation to find the slope of the tangent line to the curve at the specified point.
**+y* = 16; (1.715)
M
Sie
-0.0374
lyvis
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39
NU
Que
NU
Ques
M
Ques
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Question 40 of 43

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x
Incorrect
A conical water tower with vertex down has a radius of 10 ft at the top and is 26ft high. If water flows into the tank at a rate of 28
ft/min, how fast is the depth of the water increasing when the water is 15 ft deep?
The depth of water is increasing at a rate of 0.07
ft/min
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M
QL
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Question 42 of 43

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X
Edit
Find a horizontal line y = k that divides the area between
y = z2 and y = 49 into two equal parts.
125
k=
х
2
SEO FO 10
Vic
42
M
ora
Que
Num
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Question 43 of 43
0/1
E
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X
Incorrect
Use Newton’s Method, where needed, to approximate the x-coordinates of the intersections of the curves to nine decimal places,
and then use those approximations to approximate the area of the region that lies below the curvey = sinx and above the line
y = 0.7x, where x > 0.
A=
0.2624
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Question 34 of 43

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The figure below shows the velocity versus time curve for a rocket in outer space where the only significant force on the rocket is
from its engines. It can be shown that the mass M(t) (in slugs) of the rocket at time t seconds satisfies the equation
M(t) =
T
PARTIR
where T is the thrust (in lb) of the rocket’s engines and v is the velocity (in ft/s) of the rocket. The thrust of the first stage of certain
rocket is T = 7725667 lb. Use this value of 7 and the line segment in the figure below to estimate the mass of the rocket at time
t = 100.
20,000
(ft/s)
15.000
10.000
Velocity
5.000
20 40 60 80 100 120 140
Time 1 (s)
M(100) =
1
slugs
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