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Math Help - 2 more problems i can't quite get

  1. #1
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    2 more problems i can't quite get

    1. Suppose that .

    (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 =

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

    (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 =

    2. 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 =

    here are something to start.. then you could review the previous post since the solutions are very similar..

    f(x) = 4x^3 + 5x

    f'(x) = 12x^2 + 5
    what is f'(x)=0? (this will give you the critical points, if any)
    on what interval does f'(x) >0? <0? ( increasing or decreasing)
    on what x does f'(x) changes from negative to positive? (rel min.)
    on what x does f'(x) changes from positive to negative? (rel max.)

    f''(x) = 24x
    what is f''(x) = 0 (this will give you the inflection points, if any)
    on what interval does f''(x)>0? <0? (concave up or down)
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  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
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    someplace
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    Use another image hosting service the one you are using does not have acceptable security certificates.

    Better yet learn to use LaTeX so you don't need to post images of equations
    or learn to type clear mathematics using just ASCII charaters.

    RonL

    There has been a lot of this recently, in future I will delete all posts I find
    this problem with.
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  4. #4
    Super Member angel.white's Avatar
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    Oct 2007
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    Imageshack.us is a good site for image hosting, but I think your easiest option will be to simply learn the LaTeX

    If you hold your mouse over other formulas, it will show what that user typed to get their equation, which will help you learn it, or you can go here http://www.mathhelpforum.com/math-help/latex-help/ and read the manual.
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