Determine the intervals on which the function is concave up or down and find the value at which the inflection point occurs. y = 8x – 3x4 - (Express intervals in interval notation. Use symbols and fractions where needed.) 9. point of inflection at x = 40 interval on which function is concave up:

Calculus: Early Transcendentals
8th Edition
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Author:James Stewart
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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 function is concave up or down and find the value at which the inflection point occurs.**

Given function: \( y = 8x^5 - 3x^4 \)

*(Express intervals in interval notation. Use symbols and fractions where needed.)*

1. Point of inflection at \( x = \frac{9}{40} \)

2. Interval on which the function is **concave up**: [Input field]

3. Interval on which the function is **concave down**: [Input field]
Transcribed Image Text:**Determine the intervals on which the function is concave up or down and find the value at which the inflection point occurs.** Given function: \( y = 8x^5 - 3x^4 \) *(Express intervals in interval notation. Use symbols and fractions where needed.)* 1. Point of inflection at \( x = \frac{9}{40} \) 2. Interval on which the function is **concave up**: [Input field] 3. Interval on which the function is **concave down**: [Input field]
Determine the intervals on which the function is concave up or down and find the points of inflection.

\( f(x) = 6x^3 - 11x^2 + 7 \)

(Give your answer as a comma-separated list of points in the form (*, *). Express numbers in exact form. Use symbolic notation and fractions where needed.)

**Points of inflection:**

[Input box]

---

Determine the interval on which \( f \) is concave up.

(Give your answer as an interval in the form (*, *). Use the symbol ∞ for infinity, ∪ for combining intervals, and an appropriate type of parenthesis "(", ")", "[", "]" depending on whether the interval is open or closed. Enter ∅ if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.)

\( x \in \)

[Input box]

---

Determine the interval on which \( f \) is concave down.

(Give your answer as an interval in the form (*, *). Use the symbol ∞ for infinity, ∪ for combining intervals, and an appropriate type of parenthesis "(", ")", "[", "]" depending on whether the interval is open or closed. Enter ∅ if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.)

\( x \in \)

[Input box]
Transcribed Image Text:Determine the intervals on which the function is concave up or down and find the points of inflection. \( f(x) = 6x^3 - 11x^2 + 7 \) (Give your answer as a comma-separated list of points in the form (*, *). Express numbers in exact form. Use symbolic notation and fractions where needed.) **Points of inflection:** [Input box] --- Determine the interval on which \( f \) is concave up. (Give your answer as an interval in the form (*, *). Use the symbol ∞ for infinity, ∪ for combining intervals, and an appropriate type of parenthesis "(", ")", "[", "]" depending on whether the interval is open or closed. Enter ∅ if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.) \( x \in \) [Input box] --- Determine the interval on which \( f \) is concave down. (Give your answer as an interval in the form (*, *). Use the symbol ∞ for infinity, ∪ for combining intervals, and an appropriate type of parenthesis "(", ")", "[", "]" depending on whether the interval is open or closed. Enter ∅ if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.) \( x \in \) [Input box]
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