Suppose that
(A) Find all critical values of . (A critical value is the value of at a critical point.)
If there are no critical values, enter DNE. (DNE stands for "Do Not Exist").
If there are more than one, enter them separated by commas.
Critical value(s) =
(B) Use interval notation (not things like DNE) to indicate where is increasing.
How to enter intervals.
Increasing on
(C) Use interval notation to indicate where is decreasing.
Decreasing on
(D) Find the -coordinates of all local maxima of .
If there are no local maxima, enter DNE.
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 DNE.
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 on
(G) Use interval notation to indicate where is concave down.
Concave down on
(H) Find all inflection points of .
If there are no inflection points, enter DNE.
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 DNE.
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 -1000.
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.