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Math Help - last problem....

  1. #1
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    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.
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  2. #2
    MHF Contributor kalagota's Avatar
    Joined
    Oct 2007
    From
    Taguig City, Philippines
    Posts
    1,026
    Quote Originally Posted by abcdef View Post
    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..
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