Consider the function f(x) = x² - 7x + 10 x + 5 a. Find the first derivative. f'(x) b. List any critical values. c. Identify intervals of increase. d. Identify intervals of decrease. e. Find the second derivaitve. f"(x) when x f. Based on parts b through e, f(x) has a maximum of Y when x g. Based on parts b through e, f(x) has a minimum of Y h. Use the second derivative to identify intervals where f(x) is concave up. = i. Use the second derivative to identify intervals where f(r) is concave down.
Consider the function f(x) = x² - 7x + 10 x + 5 a. Find the first derivative. f'(x) b. List any critical values. c. Identify intervals of increase. d. Identify intervals of decrease. e. Find the second derivaitve. f"(x) when x f. Based on parts b through e, f(x) has a maximum of Y when x g. Based on parts b through e, f(x) has a minimum of Y h. Use the second derivative to identify intervals where f(x) is concave up. = i. Use the second derivative to identify intervals where f(r) is concave down.
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.CR: Chapter 3 Review
Problem 8CR
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Question
![Consider the function f(x)
=
x² - 7x + 10
x + 5
a. Find the first derivative. f'(x)
b. List any critical values.
c. Identify intervals of increase.
d. Identify intervals of decrease.
e. Find the second derivaitve. f'(x)
f. Based on parts b through e, f(x) has a maximum of
Y
when x =
when x =
Y
g. Based on parts b through e, f(x) has a minimum of
h. Use the second derivative to identify intervals where f(x) is concave up.
=
=
i. Use the second derivative to identify intervals where f(x) is concave down.
j. Use the second derivative to find any inflection points.
k. State any vertical asymptotes.
1. State any slant asymptotes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2fa2b28b-c872-4092-9782-03deb29a43d9%2Fe7da4da7-2365-47ea-a5d7-376c86b3913a%2F8nj31p6_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the function f(x)
=
x² - 7x + 10
x + 5
a. Find the first derivative. f'(x)
b. List any critical values.
c. Identify intervals of increase.
d. Identify intervals of decrease.
e. Find the second derivaitve. f'(x)
f. Based on parts b through e, f(x) has a maximum of
Y
when x =
when x =
Y
g. Based on parts b through e, f(x) has a minimum of
h. Use the second derivative to identify intervals where f(x) is concave up.
=
=
i. Use the second derivative to identify intervals where f(x) is concave down.
j. Use the second derivative to find any inflection points.
k. State any vertical asymptotes.
1. State any slant asymptotes.
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