150 100- 50 -5 - 50 -100 -150 (c) Identify x-values where f"(x) = 0. (Enter your answers as a comma-separated list.) Identify x-values where f"(x) > 0. (Enter your answer using interval notation.) Identify x-values where f"(x) < 0. (Enter your answer using interval notation.) (d) Identify x-values where f'(x) has a maximum point or a minimum point. (Enter your answers as a comma-separated list.) Identify x-values where f'(x) is increasing. (Enter your answer using interval notation.) Identify x-values where f"(x) is decreasing. (Enter your answer using interval notation.)

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.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 32CR
icon
Related questions
Question
Consider the following.
f(x) = x3 - 6x2 + 8
(a) Find f'(x) and f"(x).
f'(x) = 3x2 – 12x
f"(x) = 6x – 12
(b) Graph f(x), f'(x), and f"(x) with a graphing utility.
y
y
y
150F
150F
150-
100
100
100
50
50
50
-5
-5
-5
-50
-50-
- 50-
-100
-100-
-100-
-150
- 150
-150
150
Transcribed Image Text:Consider the following. f(x) = x3 - 6x2 + 8 (a) Find f'(x) and f"(x). f'(x) = 3x2 – 12x f"(x) = 6x – 12 (b) Graph f(x), f'(x), and f"(x) with a graphing utility. y y y 150F 150F 150- 100 100 100 50 50 50 -5 -5 -5 -50 -50- - 50- -100 -100- -100- -150 - 150 -150 150
150
100
50
-5
- 50
-100
-150
(c) Identify x-values where f"(x) = 0. (Enter your answers as a comma-separated list.)
Identify x-values where f"(x) > 0. (Enter your answer using interval notation.)
Identify x-values where f"(x) < 0. (Enter your answer using interval notation.)
(d) Identify x-values where f'(x) has a maximum point or a minimum point. (Enter your answers as a comma-separated list.)
Identify x-values where f'(x) is increasing. (Enter your answer using interval notation.)
Identify x-values where f'(x) is decreasing. (Enter your answer using interval notation.)
Transcribed Image Text:150 100 50 -5 - 50 -100 -150 (c) Identify x-values where f"(x) = 0. (Enter your answers as a comma-separated list.) Identify x-values where f"(x) > 0. (Enter your answer using interval notation.) Identify x-values where f"(x) < 0. (Enter your answer using interval notation.) (d) Identify x-values where f'(x) has a maximum point or a minimum point. (Enter your answers as a comma-separated list.) Identify x-values where f'(x) is increasing. (Enter your answer using interval notation.) Identify x-values where f'(x) is decreasing. (Enter your answer using interval notation.)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Knowledge Booster
Limits and Continuity
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill