Find the vertical and horizontal asymptotes find the

Question

1. Consider the function below. (If you need to use -∞ or ∞, enter -INFINITY or INFINITY.)

f(x) = x² / (x² - 16)

a. Find the vertical and horizontal asymptotes.

b. Find the intervals where the function is increasing.

c. Find the local maximum value.

d. Find the intervals where the function is concave up. (Enter the interval that contains smaller numbers first.)

e. Find the interval where the function is concave down.

f. Use this information to sketch the graph of f. (Do this on paper. Your instructor may ask you to turn in this graph.)

2. Consider the function below. (Round the answers to two decimal places. If you need to use -∞ or ∞, enter -INFINITY or INFINITY.)

f (x) = e^x / (8 + e^x)

a. Find the horizontal asymptotes.

b. Find the interval where the function is increasing.

c. Find the inflection point.

Find the interval where the function is concave up.

Find the interval where the function is concave down.

d. Use this information to sketch the graph of f. (Do this on paper. Your instructor may ask you to turn in this graph.)