p ## Problem StatementDetermine the intervals on which the given function is concave up or concave down and find the points of inflection.\[ f(x) = 4xe^{-7x} \](Use symbolic notation and fractions where needed. Give your answer as a comma-separated list of points in the form \((\ast, \ast)\). Enter DNE if there are no points of inflection.)**Points of Inflection:**[Text box for input]---### Determine the interval on which \( f \) is concave up.(Use symbolic notation and fractions where needed. Give your answer as an interval in the form \((\ast, \ast)\). Use the symbol \(\infty\) for infinity, \( U \) for combining intervals, and an appropriate type of parenthesis "\(", "\)", "\(", "\]", depending on whether the interval is open or closed. Enter \(\emptyset\) if the interval is empty.)\[ x \in \][Text box for input]---### Determine the interval on which \( f \) is concave down.(Use symbolic notation and fractions where needed. Give your answer as an interval in the form \((\ast, \ast)\). Use the symbol \(\infty\) for infinity, \( U \) for combining intervals, and an appropriate type of parenthesis "\(", "\)", "\(", "\]", depending on whether the interval is open or closed. Enter \(\emptyset\) if the interval is empty.)\[ x \in \][Text box for input]

Answered: Image /qna-images/answer/5c0286f6-1e01-4472-9622-b72ed8bdfed8.jpg

termine the intervals on which the given function is concave up or concave down and find the points of inflection. S(x) = 4xe-7x se symbolic notation and fractions where needed. Give your answer as a comma separated list of points in the form in the m (*, *). Enter DNE if there are no points of inflection.) points of inflection: etermine the interval on which ƒ is concave up. se symbolic notation and fractions where needed. Give your answer as interval in the form (*, *). Use the symbol o for inity, U for combining intervals, and an appropriate type of parenthesis "(", ")", "[". "J" depending on whether the interval is en or closed. Enter ø if the interval is empty.) x€ termine the interval on which f is concave down. se symbolic notation and fractions where needed. Give your answer as interval in the form (*, *). Use the symbol o for inity, U for combining intervals, and an appropriate type of parenthesis "(". ")". "I". "]" depending on whether the interval is en or closed. Enter Ø if the interval is empty.) xE