Given f(x) = (6x)/(x^2 - 9), find intercepts, asymptotes, limits, intervals of...

[onty5577]

Stuck with problem. Can someone please help?

Answer the following questions regarding the function below, and use your answers to sketch the function.

. . . . .\(\displaystyle f(x)\, =\, \dfrac{6x}{x^2\, -\, 9}\)

1. List the x-values of any x-intercepts of f.

2. Give the y-value of the y-intercept of f.

3. List the x-values of any vertical asymptotes of f.

4. Evaluate the following limits:

. . . . .\(\displaystyle \displaystyle \mbox{a. }\, \lim_{x \rightarrow \infty}\, f(x)\)

. . . . .\(\displaystyle \displaystyle \mbox{b. }\, \lim_{x \rightarrow -\infty}\, f(x)\)

5. List the y-values of any horizontal asymptotes of f.

6. Find the intervals on which f is increasing or decreasing.

7. List the coordinates of any local extrema.

8. Find the intervals on which f is concave up or concave down.

9. List the coordinates of any points of inflection.

 

[Deleted member 4993]

Stuck with problem. Can someone please help?

Answer the following questions regarding the function below, and use your answers to sketch the function.

. . . . .\(\displaystyle f(x)\, =\, \dfrac{6x}{x^2\, -\, 9}\)

1. List the x-values of any x-intercepts of f.

2. Give the y-value of the y-intercept of f.

3. List the x-values of any vertical asymptotes of f.

4. Evaluate the following limits:

. . . . .\(\displaystyle \displaystyle \mbox{a. }\, \lim_{x \rightarrow \infty}\, f(x)\)

. . . . .\(\displaystyle \displaystyle \mbox{b. }\, \lim_{x \rightarrow -\infty}\, f(x)\)

5. List the y-values of any horizontal asymptotes of f.

6. Find the intervals on which f is increasing or decreasing.

7. List the coordinates of any local extrema.

8. Find the intervals on which f is concave up or concave down.

9. List the coordinates of any points of inflection.

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

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[stapel]

Stuck with problem. Can someone please help?

At which point are you stuck? How are you stuck?

Answer the following questions regarding the function below, and use your answers to sketch the function.

. . . . .\(\displaystyle f(x)\, =\, \dfrac{6x}{x^2\, -\, 9}\)

1. List the x-values of any x-intercepts of f.

2. Give the y-value of the y-intercept of f.

Finding intercepts is just algebra. (here) Where are you getting bogged down in the plugging-zero-in-and-solving process?

3. List the x-values of any vertical asymptotes of f.

4. Evaluate the following limits:

. . . . .\(\displaystyle \displaystyle \mbox{a. }\, \lim_{x \rightarrow \infty}\, f(x)\)

. . . . .\(\displaystyle \displaystyle \mbox{b. }\, \lim_{x \rightarrow -\infty}\, f(x)\)

5. List the y-values of any horizontal asymptotes of f.

Finding asymptotes is from algebra (and the limit stuff above is just the calculus version of the algebra rules). (here) Where are you stuck in the process?

6. Find the intervals on which f is increasing or decreasing.

What did you see when you graphed this in your calculator? What did you determine from the First Derivative Test?

7. List the coordinates of any local extrema.

The extrema are at the zeroes of the first derivative. What did you get?

8. Find the intervals on which f is concave up or concave down.

What did you see when you graphed this in your calculator? What did you determine from the Second Derivative Test?

9. List the coordinates of any points of inflection.

The inflection points are at the zeroes of the second derivative. What did you get?

Please be complete. Thank you!