1. last problem....

Suppose that .

Note: Several parts of this problem require answers entered in interval notation. Note, with interval notation, you can enter the empty set as .

(A) List all the critical values of . Note: If there are no critical values, enter NONE.

(B) Use interval notation to indicate where is increasing.
Increasing:
(C) Use interval notation to indicate where is decreasing.
Decreasing:
(D) List the values of all local maxima of . If there are no local maxima, enter NONE.
values of local maximums =
(E) List the values of all local minima of . If there are no local minima, enter NONE.
values of local minimums =
(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) List the values of all the inflection points of . If there are no inflection points, enter NONE.
values of inflection points = (I) Use all of the preceding information to sketch a graph of . Include all vertical and/or horizontal asymptotes. When you're finished, enter a "1" in the box below.

2. Originally Posted by abcdef
Suppose that .

Note: Several parts of this problem require answers entered in interval notation. Note, with interval notation, you can enter the empty set as .

(A) List all the critical values of . Note: If there are no critical values, enter NONE.

(B) Use interval notation to indicate where is increasing.
Increasing:
(C) Use interval notation to indicate where is decreasing.
Decreasing:
(D) List the values of all local maxima of . If there are no local maxima, enter NONE.
values of local maximums =
(E) List the values of all local minima of . If there are no local minima, enter NONE.
values of local minimums =
(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) List the values of all the inflection points of . If there are no inflection points, enter NONE.
values of inflection points = (I) Use all of the preceding information to sketch a graph of . Include all vertical and/or horizontal asymptotes. When you're finished, enter a "1" in the box below.
$f(x) = 12 - 6 ln x$, x>0

a) $f'(x) = \frac{-6}{x} = 0$
so, there is no crit value.

x>0 which means $\frac{-6}{x} <0$
b) it is not increasing
c) it is decreasing in the domain $(0, \infty)$

d , e) no local extrema

$f''(x) = \frac{6}{x^2}$ which is positive for all x>0
f, g) always concave up

h) no point of inflection

vertical asymptote is x=0.. sketch it.. Ü