"(x). "'(x). "(-9) and f"(7). = f(x) = x³ 3x² +7 mine whether the function f(x) is concave up or concave down at the indicated points. x = -9 x = 7 concave up concave down concave up concave down
"(x). "'(x). "(-9) and f"(7). = f(x) = x³ 3x² +7 mine whether the function f(x) is concave up or concave down at the indicated points. x = -9 x = 7 concave up concave down concave up concave down
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
![Consider the function.
\[ f(x) = x^3 - 3x^2 + 7 \]
Find \( f'(x) \).
\[ f'(x) = \]
Find \( f''(x) \).
\[ f''(x) = \]
Find \( f''(-9) \) and \( f''(7) \).
\[ f''(-9) = \]
\[ f''(7) = \]
Determine whether the function \( f(x) \) is concave up or concave down at the indicated points.
(a) \( x = -9 \)
- ○ concave up
- ○ concave down
(b) \( x = 7 \)
- ○ concave up
- ○ concave down](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F125111cc-25a5-4f05-886d-ef1bfa459fc8%2F2b3d6a84-13c7-4543-8d62-fb375fc8d27d%2Fso5tpdg_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the function.
\[ f(x) = x^3 - 3x^2 + 7 \]
Find \( f'(x) \).
\[ f'(x) = \]
Find \( f''(x) \).
\[ f''(x) = \]
Find \( f''(-9) \) and \( f''(7) \).
\[ f''(-9) = \]
\[ f''(7) = \]
Determine whether the function \( f(x) \) is concave up or concave down at the indicated points.
(a) \( x = -9 \)
- ○ concave up
- ○ concave down
(b) \( x = 7 \)
- ○ concave up
- ○ concave down
Expert Solution
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Step 1
Topic:- derivatives and application of derivatives
Definition:-
When the second derivative is positive, the function is concave upward. When the second derivative is negative, the function is concave downward.
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