F(x) = x- 16x3+ 72x2 + 4 (a) Make a sign diagram for the first derivative. f"x) <0 F'(x) > 0 F"(x) > 0 F'(x) <0 F'(x) <0 %3D (b) Make a sign diagram for the second derivative. "x) > 0 V "(x) <0 "x) <0 "X) = 0 V ["(x) > 0 (c) Sketch the graph, showing all relative extreme points and inflection points. y 400 400 IP 200 IP 200 -6 -4 -2 2 4 6. -6 -4 -2 4 6. IP -200 -200 IP 400 400 y y 400 400 IP 200 IP 200 -6 -4 -2 6. -6 -4 -2 4. 6. IP 200

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.4: Operations On Functions
Problem 124E
Topic Video
Question
Please correct me answer both each blank answered thanks
Consider the following function.
F(x) = x* - 16x + 72x2 + 4
(a) Make a sign diagram for the first derivative.
FX) <0
F'(x) > 0 VX
F(x) >0 V
F'(x) < 0
V x
F'(x) < 0 VX
x%3D
(b) Make a sign diagram for the second derivative.
f "(x) >0
F"(x) < 0
VX
F"(x) < 0 Vv
E"(x) = 0 V
F"(x) > 0
V
(c) Sketch the graph, showing all relative extreme points and inflection points.
y
y
400
400
IP
200
200
IP
-6
-4
-2
2
4
-6
-4
-2
2.
4
IP -200
-200
IP
400
-400
y
y
400
9 IP
400
200
IP
200
-6
-4
-2
2.
4 6
-6
-4
-2
4
IP
200
-200
Transcribed Image Text:Consider the following function. F(x) = x* - 16x + 72x2 + 4 (a) Make a sign diagram for the first derivative. FX) <0 F'(x) > 0 VX F(x) >0 V F'(x) < 0 V x F'(x) < 0 VX x%3D (b) Make a sign diagram for the second derivative. f "(x) >0 F"(x) < 0 VX F"(x) < 0 Vv E"(x) = 0 V F"(x) > 0 V (c) Sketch the graph, showing all relative extreme points and inflection points. y y 400 400 IP 200 200 IP -6 -4 -2 2 4 -6 -4 -2 2. 4 IP -200 -200 IP 400 -400 y y 400 9 IP 400 200 IP 200 -6 -4 -2 2. 4 6 -6 -4 -2 4 IP 200 -200
fx) = x - 9x + 27x + 8
(a) Make a sign diagram for the first derivative.
Select- V
Select-
--Select- V
(b) Make a sign diagram for the second derivative.
Select-- V
Select--V
Select--- V
(c) Sketch the graph, showing all relative extreme points and inflection points.
y
40
40
40
IP
20
20
20
2.
-2
-4
-2
-20
20
20
IP
IP
40
-40
-40
40
IP
Transcribed Image Text:fx) = x - 9x + 27x + 8 (a) Make a sign diagram for the first derivative. Select- V Select- --Select- V (b) Make a sign diagram for the second derivative. Select-- V Select--V Select--- V (c) Sketch the graph, showing all relative extreme points and inflection points. y 40 40 40 IP 20 20 20 2. -2 -4 -2 -20 20 20 IP IP 40 -40 -40 40 IP
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