Determine the intervals on which the given function is concave up or concave down and find the points of inflection. f(x) = (x – 6)(1 – x³) (Use symbolic notation and fractions where needed. Give your answer as a comma separated list of points in the form in the form (*, *). 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 co for infinity, U for combining intervals, and an appropriate type of parenthesis "(", ")", "[", or "]", depending on whether the interval is 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) = (x – 6)(1 – x³) (Use symbolic notation and fractions where needed. Give your answer as a comma separated list of points in the form in the form (*, *). 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 co for infinity, U for combining intervals, and an appropriate type of parenthesis "(", ")", "[", or "]", depending on whether the interval is 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**
Given Function:
\[ f(x) = (x - 6)(1 - x^3) \]
For this exercise, use symbolic notation and fractions as 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) =**
\[ \underline{\hspace{12cm}} \]
*Note: Use symbolic notation and fractions where necessary. Your answers should be given as intervals in the form \((*, *)\). Use \(\infty\) for infinity, \( \cup \) for combining intervals, and choose the appropriate type of parenthesis \("(", ")", "[", "}"\), depending on whether the interval is open or closed. Enter \(\emptyset\) if the interval is empty.*
**Concavity**
\( f \) is concave up when \( x \in \)
\[ \underline{\hspace{12cm}} \]
\( f \) is concave down when \( x \in \)
\[ \underline{\hspace{12cm}} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd31682c5-2fc9-464e-9dc7-0f0389d48dd3%2F7fc52344-2994-43d9-b7a3-dbb143fe24ad%2F63y1l6p_processed.png&w=3840&q=75)
Transcribed Image Text:**Determine the Intervals of Concavity and Points of Inflection**
Given Function:
\[ f(x) = (x - 6)(1 - x^3) \]
For this exercise, use symbolic notation and fractions as 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) =**
\[ \underline{\hspace{12cm}} \]
*Note: Use symbolic notation and fractions where necessary. Your answers should be given as intervals in the form \((*, *)\). Use \(\infty\) for infinity, \( \cup \) for combining intervals, and choose the appropriate type of parenthesis \("(", ")", "[", "}"\), depending on whether the interval is open or closed. Enter \(\emptyset\) if the interval is empty.*
**Concavity**
\( f \) is concave up when \( x \in \)
\[ \underline{\hspace{12cm}} \]
\( f \) is concave down when \( x \in \)
\[ \underline{\hspace{12cm}} \]
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