Consider the following function. f(x) = x4 16x³ + 72x² + 8 (a) Make a sign diagram for the first derivative. ---Select--- X ---Select--- X X = X (b) Make a sign diagram for the second derivative. ---Select--- ✓ X ---Select--- X X X = ---Select--- X ---Select--- X X = X = ---Select--- X ---Select--- ✓ (c) Sketch the graph, showing all relative extreme points and inflection points. X X ---Select--- ✓ X ---Select--- ✓ X

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.5: Graphical Differentiation
Problem 2E
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Consider the following function.
f(x) = x4 16x³ + 72x² +8
(a) Make a sign diagram for the first derivative.
---Select--- X
---Select--- X
X =
(b) Make a sign diagram for the second derivative.
---Select--- X
---Select--- ✓X
X =
-Select--- ✓X
---Select--x
x =
X =
(c) Sketch the graph, showing all relative extreme points and inflection points.
--Select--- X
--Select--x
X
X
--Select--- ✓ X
---Select--- X
Transcribed Image Text:Consider the following function. f(x) = x4 16x³ + 72x² +8 (a) Make a sign diagram for the first derivative. ---Select--- X ---Select--- X X = (b) Make a sign diagram for the second derivative. ---Select--- X ---Select--- ✓X X = -Select--- ✓X ---Select--x x = X = (c) Sketch the graph, showing all relative extreme points and inflection points. --Select--- X --Select--x X X --Select--- ✓ X ---Select--- X
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