Suppose that
(A) Find all critical values of .
If there are no critical values, enter
None.
If there are more than one, enter them separated by commas.
Critical value(s) =
(B) Use
interval notation to indicate where is increasing. If it is increasing on more than one interval, enter the union of all intervals where is increasing.
Increasing:
(C) Use
interval notation to indicate where is decreasing. If it is decreasing on more than one interval, enter the union of all intervals where is decreasing.
Decreasing:
(D) Find the -coordinates of all local maxima of .
If there are no local maxima, enter
None.
If there are more than one, enter them separated by commas.
Local maxima at =
(E) Find the -coordinates of all local minima of .
If there are no local minima, enter
None.
If there are more than one, enter them separated by commas.
Local minima at =
(F) Use
interval notation to indicate where is concave up.
Concave up:
(G) Use
interval notation to indicate where is concave down.
Concave down:
(H) Find all inflection points of .
If there are no inflection points, enter
None.
If there are more than one, enter them separated by commas.
Inflection point(s) at =
(I) Find all horizontal asymptotes of .
If there are no horizontal asymptotes, enter
None.
If there are more than one, enter them separated by commas.
Horizontal asymptote(s): =
(J) Find all vertical asymptotes of .
If there are no vertical asymptotes, enter
None.
If there are more than one, enter them separated by commas.
Vertical asymptote(s): =
(K) Use all of the preceding information to sketch a
graph of . When you're finished, enter a
1 in the box
below.
Graph Complete:
You can earn partial credit on this problem.