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

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

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

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:

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

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

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.

2. Originally Posted by onty5577

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

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:

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

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

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.

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

If you are stuck at the beginning tell us and we'll start with the definitions.

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3. Originally Posted by onty5577
At which point are you stuck? How are you stuck?

Originally Posted by onty5577

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

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?

Originally Posted by onty5577
3. List the x-values of any vertical asymptotes of f.

4. Evaluate the following limits:

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

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

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?

Originally Posted by onty5577
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?

Originally Posted by onty5577
7. List the coordinates of any local extrema.
The extrema are at the zeroes of the first derivative. What did you get?

Originally Posted by onty5577
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?

Originally Posted by onty5577
9. List the coordinates of any points of inflection.
The inflection points are at the zeroes of the second derivative. What did you get?