Consider the following function. (If an answer does not exist, enter DNE.)

f(x) = 1 +7/x-4/x'2

Find the vertical asymptote(s). (Enter your answers as a comma-separated list.)

x =

Find the horizontal asymptote(s). (Enter your answers as a comma-separated list.)

y =

(b) Find the interval where the function is increasing. (Enter your answer using interval notation.)

Find the interval where the function is decreasing. (Enter your answer using interval notation.)

(c) Find the local maximum and minimum values.

local maximum value local minimum value

(d) Find the interval where the function is concave up. (Enter your answer using interval notation.)

Find the interval where the function is concave down. (Enter your answer using interval notation.)

Find the inflection point.

(x, y) =

2--Consider the following.

B(x)=3x'2/3-x

(a) Find the interval of increase. (Enter your answer using interval notation.)

Find the interval of decrease. (Enter your answer using interval notation.)

(b) Find the local maximum value(s). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

Find the local minimum value(s). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

(c) Find the interval where the graph is concave downward. (Enter your answer using interval notation.)

3-Find the x-coordinate(s) of the inflection point(s) of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

15x'2+Inx(x>0)

a inflection point(s) at x =

b-Determine the intervals on which the function is concave up or concave down. (Enter your answers using interval notation. Enter EMPTY or for the empty set.)

concave up concave down

4- Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)

y=In(x'2+36)'1/2

a (x, y) = b (smaller x-value)(x, y) =

c (larger x-value)=

5 Determine the intervals on which the function is concave up or concave down. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)

f() = 22 + 22 sin²(),[0, ]

concave up concave down