(A) List all critical numbers of f. If there are no critical numbers, enter 'NONE'. Critical numbers = NONE (B) Use interval notation to indicate where f(x) is decreasing. Note: Use 'INF' for ∞o, '-INF' for-co, and use 'U' for the union symbol. Decreasing: (-inf,3)U(-3,3)U(3,inf) (C)List the x-values of all local maxima of f. If there are no local maxima, enter 'NONE'. x values of local maxima = NONE (D) List the x-values of all local minima of f. If there are no local minima, enter 'NONE'. x values of local minima = NONE (F) Use interval notation to indicate where f(x) is concave up. Concave up: f(x) = (E) List the x values of all inflection points of f. If there are no inflection points, enter 'NONE'. Inflection points = (G) Use interval notation to indicate where f(x) is concave down. Concave down: 5x x²-9 (1) List all vertical asymptotes of f. If there are no vertical asymptotes, enter 'NONE'. vertical asymptotes x = (H) List all horizontal asymptotes of f. If there are no horizontal asymptotes, enter 'NONE'. Horizontal asymptotes y = Loe all. of the pres nation to akatak graph
(A) List all critical numbers of f. If there are no critical numbers, enter 'NONE'. Critical numbers = NONE (B) Use interval notation to indicate where f(x) is decreasing. Note: Use 'INF' for ∞o, '-INF' for-co, and use 'U' for the union symbol. Decreasing: (-inf,3)U(-3,3)U(3,inf) (C)List the x-values of all local maxima of f. If there are no local maxima, enter 'NONE'. x values of local maxima = NONE (D) List the x-values of all local minima of f. If there are no local minima, enter 'NONE'. x values of local minima = NONE (F) Use interval notation to indicate where f(x) is concave up. Concave up: f(x) = (E) List the x values of all inflection points of f. If there are no inflection points, enter 'NONE'. Inflection points = (G) Use interval notation to indicate where f(x) is concave down. Concave down: 5x x²-9 (1) List all vertical asymptotes of f. If there are no vertical asymptotes, enter 'NONE'. vertical asymptotes x = (H) List all horizontal asymptotes of f. If there are no horizontal asymptotes, enter 'NONE'. Horizontal asymptotes y = Loe all. of the pres nation to akatak graph
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Analysis of the Function \(f(x) = \frac{5x}{x^2 - 9}\)
This exercise involves a detailed analysis of the function \(f(x) = \frac{5x}{x^2 - 9}\). Follow the steps below to extract critical information about this function.
#### (A) List all critical numbers of \(f\).
If there are no critical numbers, enter ‘NONE’.
* **Critical numbers**: NONE
#### (B) Use interval notation to indicate where \(f(x)\) is decreasing.
**Note**: Use ‘INF’ for \(\infty\), ‘-INF’ for \(-\infty\), and use ‘U’ for the union symbol.
* **Decreasing:** (-inf,-3)U(-3,3)U(3,inf)
#### (C) List the \(x\)-values of all local maxima of \(f\).
If there are no local maxima, enter ‘NONE’.
* **x-values of local maxima**: NONE
#### (D) List the \(x\)-values of all local minima of \(f\).
If there are no local minima, enter ‘NONE’.
* **x-values of local minima**: NONE
#### (E) List the \(x\)-values of all inflection points of \(f\).
If there are no inflection points, enter ‘NONE’.
* **Inflection points:** [Your Answer Here]
#### (F) Use interval notation to indicate where \(f(x)\) is concave up.
* **Concave up:** [Your Answer Here]
#### (G) Use interval notation to indicate where \(f(x)\) is concave down.
* **Concave down:** [Your Answer Here]
#### (H) List all horizontal asymptotes of \(f\).
If there are no horizontal asymptotes, enter ‘NONE’.
* **Horizontal asymptotes:** y = [Your Answer Here]
#### (I) List all vertical asymptotes of \(f\).
If there are no vertical asymptotes, enter ‘NONE’.
* **Vertical asymptotes:** x = [Your Answer Here]
#### (J) Use all of the preceding information to sketch a graph of \(f\).
When you’re finished, enter a “1” in the box below.
* [Sketch your graph here]
Use the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3a780900-9b69-4fe9-9f43-185066935266%2F96811c29-acfd-4cd4-ac39-5945bf5e7d0a%2Frr9yhh3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Analysis of the Function \(f(x) = \frac{5x}{x^2 - 9}\)
This exercise involves a detailed analysis of the function \(f(x) = \frac{5x}{x^2 - 9}\). Follow the steps below to extract critical information about this function.
#### (A) List all critical numbers of \(f\).
If there are no critical numbers, enter ‘NONE’.
* **Critical numbers**: NONE
#### (B) Use interval notation to indicate where \(f(x)\) is decreasing.
**Note**: Use ‘INF’ for \(\infty\), ‘-INF’ for \(-\infty\), and use ‘U’ for the union symbol.
* **Decreasing:** (-inf,-3)U(-3,3)U(3,inf)
#### (C) List the \(x\)-values of all local maxima of \(f\).
If there are no local maxima, enter ‘NONE’.
* **x-values of local maxima**: NONE
#### (D) List the \(x\)-values of all local minima of \(f\).
If there are no local minima, enter ‘NONE’.
* **x-values of local minima**: NONE
#### (E) List the \(x\)-values of all inflection points of \(f\).
If there are no inflection points, enter ‘NONE’.
* **Inflection points:** [Your Answer Here]
#### (F) Use interval notation to indicate where \(f(x)\) is concave up.
* **Concave up:** [Your Answer Here]
#### (G) Use interval notation to indicate where \(f(x)\) is concave down.
* **Concave down:** [Your Answer Here]
#### (H) List all horizontal asymptotes of \(f\).
If there are no horizontal asymptotes, enter ‘NONE’.
* **Horizontal asymptotes:** y = [Your Answer Here]
#### (I) List all vertical asymptotes of \(f\).
If there are no vertical asymptotes, enter ‘NONE’.
* **Vertical asymptotes:** x = [Your Answer Here]
#### (J) Use all of the preceding information to sketch a graph of \(f\).
When you’re finished, enter a “1” in the box below.
* [Sketch your graph here]
Use the
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