Determine the intervals on which the given function is concave up or concave down and find the points of inflection. f(x) 12)(1 – x³) = (x - Use symbolic notation and fractions where needed. Give your answer as a comma separated list of points in the form in the orm (*, *). Enter DNE if there are no points of inflection.) points of inflection: (x, y) = Use symbolic notation and fractions where needed. Give your answers as intervals in the form (*, *). Use the symbol o for nfinity, U for combining intervals, and an appropriate type of parenthesis "(", ")", "[", or "]", depending on whether the interval s open or closed. Enter Ø if the interval is empty.) f is concave up when x E f is concave down when x E
Determine the intervals on which the given function is concave up or concave down and find the points of inflection. f(x) 12)(1 – x³) = (x - Use symbolic notation and fractions where needed. Give your answer as a comma separated list of points in the form in the orm (*, *). Enter DNE if there are no points of inflection.) points of inflection: (x, y) = Use symbolic notation and fractions where needed. Give your answers as intervals in the form (*, *). Use the symbol o for nfinity, U for combining intervals, and an appropriate type of parenthesis "(", ")", "[", or "]", depending on whether the interval s open or closed. Enter Ø if the interval is empty.) f is concave up when x E f is concave down when x E
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...
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![### Determine the Intervals of Concavity and Points of Inflection
#### Function:
\[ f(x) = (x - 12)(1 - x^3) \]
(Use symbolic notation and fractions where needed. Provide your answer as a comma-separated list of points in the form (\*, \*). Enter DNE if there are no points of inflection.)
#### Points of Inflection:
\[ (x, y) = \text{[Input Box]} \]
---
(Use symbolic notation and fractions where needed. Answer the intervals in the form (\*, \*). Use the symbol \(\infty\) for infinity, \(\cup\) for combining intervals, and appropriately choose between parentheses "\(", "\)", "\[", or "\]" to indicate whether the interval is open or closed. Enter \(\emptyset\) if the interval is empty.)
#### Concavity:
- **\( f \) is concave up when \( x \in \)**
\[ \text{[Input Box]} \]
- **\( f \) is concave down when \( x \in \)**
\[ \text{[Input Box]} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd5e6f7d9-13e2-4805-b19c-efff4c4b26c6%2F80931a71-ce2e-4440-8af0-fd5410412550%2Fmszj4rn_processed.png&w=3840&q=75)
Transcribed Image Text:### Determine the Intervals of Concavity and Points of Inflection
#### Function:
\[ f(x) = (x - 12)(1 - x^3) \]
(Use symbolic notation and fractions where needed. Provide your answer as a comma-separated list of points in the form (\*, \*). Enter DNE if there are no points of inflection.)
#### Points of Inflection:
\[ (x, y) = \text{[Input Box]} \]
---
(Use symbolic notation and fractions where needed. Answer the intervals in the form (\*, \*). Use the symbol \(\infty\) for infinity, \(\cup\) for combining intervals, and appropriately choose between parentheses "\(", "\)", "\[", or "\]" to indicate whether the interval is open or closed. Enter \(\emptyset\) if the interval is empty.)
#### Concavity:
- **\( f \) is concave up when \( x \in \)**
\[ \text{[Input Box]} \]
- **\( f \) is concave down when \( x \in \)**
\[ \text{[Input Box]} \]
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