Determine the intervals on which the graph of y = f(x) is concave up or concave down, and find the x-values at which the points of inflection occur. f(x) = x(x – 7 x), x > 0 (Enter an exact answer. Use symbolic notation and fractions where needed. Give your answer in the form of a comma separate list, if necessary. Enter DNE if there are no points of inflection.) x = (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 interv is open or closed. Enter Ø if the interval is empty.)
Determine the intervals on which the graph of y = f(x) is concave up or concave down, and find the x-values at which the points of inflection occur. f(x) = x(x – 7 x), x > 0 (Enter an exact answer. Use symbolic notation and fractions where needed. Give your answer in the form of a comma separate list, if necessary. Enter DNE if there are no points of inflection.) x = (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 interv is open or closed. Enter Ø if the interval is empty.)
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 on which the graph of \( y = f(x) \) is concave up or concave down, and find the \( x \)-values at which the points of inflection occur.
\[ f(x) = x(x - 7\sqrt{x}), \quad x > 0 \]
(Enter an exact answer. Use symbolic notation and fractions where needed. Give your answer in the form of a comma separated list, if necessary. Enter DNE if there are no points of inflection.)
\[ x = \]
(Use symbolic notation and fractions where needed. Give your answers as intervals in the form \((\ast, \ast)\). Use the symbol \(\infty\) for infinity, \(\cup\) for combining intervals, and an appropriate type of parenthesis "\((\)", "\()]", "\([)", or "\([]\)", depending on whether the interval is open or closed. Enter \(\emptyset\) if the interval is empty.)
\( f \) is concave up when \( x \in \)
\[ \]
\( f \) is concave down when \( x \in \)
\[ \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fd7061d-729c-4718-a2e7-fb53d4373f92%2F89e6096c-d989-4b53-ad89-5b9eb5b4da69%2F75itlk_processed.png&w=3840&q=75)
Transcribed Image Text:Determine the intervals on which the graph of \( y = f(x) \) is concave up or concave down, and find the \( x \)-values at which the points of inflection occur.
\[ f(x) = x(x - 7\sqrt{x}), \quad x > 0 \]
(Enter an exact answer. Use symbolic notation and fractions where needed. Give your answer in the form of a comma separated list, if necessary. Enter DNE if there are no points of inflection.)
\[ x = \]
(Use symbolic notation and fractions where needed. Give your answers as intervals in the form \((\ast, \ast)\). Use the symbol \(\infty\) for infinity, \(\cup\) for combining intervals, and an appropriate type of parenthesis "\((\)", "\()]", "\([)", or "\([]\)", depending on whether the interval is open or closed. Enter \(\emptyset\) if the interval is empty.)
\( f \) is concave up when \( x \in \)
\[ \]
\( f \) is concave down when \( x \in \)
\[ \]
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