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Consider the function f(x) = 7x² - 6x² - 6. Identify the locations where f has transition points, the intervals of increase, decrease, and the intervals where fis concave up and concave down. (For any interval, give your answers as intervals in the form (, *). Use the symbol oo for infinity, U for combining intervals, and an appropriate type of parentheses "C".")", "[", or "J" depending on whether the interval is open or closed. Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNE if no such interval exists. When identifying the location(s) of the transition point(s), if multiple points exist, separate each x-value with a comma and enter DNE if no such x-value exists.) √/21 f has a local maximum at x = Incorrect f has a local minimum at x = Incorrect f is increasing on: f is decreasing on: f has a point of inflection at x = Incorrect 21 (0° ^)^(0^-) (-.-VT) (0.VT) (-4--4) (-4) Parentheses around lists are not accepted

Consider the function f(x) = 7x² - 6x² - 6. Identify the locations where f has transition points, the intervals of increase, decrease, and the intervals where fis concave up and concave down. (For any interval, give your answers as intervals in the form (, *). Use the symbol oo for infinity, U for combining intervals, and an appropriate type of parentheses "C".")", "[", or "J" depending on whether the interval is open or closed. Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNE if no such interval exists. When identifying the location(s) of the transition point(s), if multiple points exist, separate each x-value with a comma and enter DNE if no such x-value exists.) √/21 f has a local maximum at x = Incorrect f has a local minimum at x = Incorrect f is increasing on: f is decreasing on: f has a point of inflection at x = Incorrect 21 (0° ^)^(0^-) (-.-VT) (0.VT) (-4--4) (-4) Parentheses around lists are not accepted

Calculus: Early Transcendentals
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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please do the graph as well thank you 

### Analysis of Function for Transition Points, Increase/Decrease Intervals, and Concavity Consider the function \( f(x) = 7x^4 - 6x^3 - 6 \). Identify the locations where \( f \) has transition points, the intervals of increase, decrease, and the intervals where \( f \) is concave up and concave down. **Instructions:** - For any interval, give your answers as intervals in the form \( (a, b) \). - Use the symbol \( \infty \) for infinity. - Use \( \cup \) for combining intervals. - Use symbolic notation and fractions where needed. Express numbers in exact form. - Assume the variables \( x \), \( f(x) \), etc., as necessary. - When identifying transition points, if multiple points exist, separate each \( x \)-value with a comma and enter DNE if no such \( x \)-value exists. --- 1. **Local Maxima:** \( f \) has a local maximum at \( x = \boxed{\frac{\sqrt{71}}{7} - \frac{51}{7}} \) *(Incorrect)* 2. **Local Minima:** \( f \) has a local minimum at \( x = \boxed{\frac{\sqrt{71}}{7} - \frac{51}{7}} \) *(Incorrect)* 3. **Increasing Intervals:** \( f \) is increasing on \( \left( \boxed{-\frac{\sqrt{71}}{7}}, 0 \right) \cup \left( 0, \boxed{\frac{\sqrt{71}}{7}} \right) \) 4. **Decreasing Intervals:** \( f \) is decreasing on \( \left( -\infty, \boxed{-\frac{\sqrt{71}}{7}} \right) \cup \left( \boxed{\frac{\sqrt{71}}{7}}, \infty \right) \) 5. **Points of Inflection:** \( f \) has a point of inflection at \( x = \boxed{\left( \frac{\sqrt{7}}{7} - \frac{49}{7}, \frac{\sqrt{7}}{7} + \frac{49}{7} \right)} \) *(Parentheses around lists are
Transcribed Image Text:### Analysis of Function for Transition Points, Increase/Decrease Intervals, and Concavity Consider the function \( f(x) = 7x^4 - 6x^3 - 6 \). Identify the locations where \( f \) has transition points, the intervals of increase, decrease, and the intervals where \( f \) is concave up and concave down. **Instructions:** - For any interval, give your answers as intervals in the form \( (a, b) \). - Use the symbol \( \infty \) for infinity. - Use \( \cup \) for combining intervals. - Use symbolic notation and fractions where needed. Express numbers in exact form. - Assume the variables \( x \), \( f(x) \), etc., as necessary. - When identifying transition points, if multiple points exist, separate each \( x \)-value with a comma and enter DNE if no such \( x \)-value exists. --- 1. **Local Maxima:** \( f \) has a local maximum at \( x = \boxed{\frac{\sqrt{71}}{7} - \frac{51}{7}} \) *(Incorrect)* 2. **Local Minima:** \( f \) has a local minimum at \( x = \boxed{\frac{\sqrt{71}}{7} - \frac{51}{7}} \) *(Incorrect)* 3. **Increasing Intervals:** \( f \) is increasing on \( \left( \boxed{-\frac{\sqrt{71}}{7}}, 0 \right) \cup \left( 0, \boxed{\frac{\sqrt{71}}{7}} \right) \) 4. **Decreasing Intervals:** \( f \) is decreasing on \( \left( -\infty, \boxed{-\frac{\sqrt{71}}{7}} \right) \cup \left( \boxed{\frac{\sqrt{71}}{7}}, \infty \right) \) 5. **Points of Inflection:** \( f \) has a point of inflection at \( x = \boxed{\left( \frac{\sqrt{7}}{7} - \frac{49}{7}, \frac{\sqrt{7}}{7} + \frac{49}{7} \right)} \) *(Parentheses around lists are
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