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Math Help - inflection points

  1. #1
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    inflection points

    Let f(x)= -x^4-7x^3+8x+3.
    (A) Use interval notation to indicate where is concave up.
    Note: Use 'INF' for , '-INF' for , and use 'U' for the union symbol.
    Concave up:

    (B) Use interval notation to indicate where f(x) is concave down.
    Concave down:
    (C) 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
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    Quote Originally Posted by abcdef View Post
    Let f(x)= -x^4-7x^3+8x+3.
    (A) Use interval notation to indicate where is concave up.
    Note: Use 'INF' for , '-INF' for , and use 'U' for the union symbol.
    Concave up:

    (B) Use interval notation to indicate where f(x) is concave down.
    Concave down:
    (C) List the values of all the inflection points of . If there are no inflection points, enter 'NONE'.
    values of inflection points =
    f(x) = -x^4 - 7x^3 + 8x + 3

    f'(x) = -4x^3 - 21x^2 + 8

    f''(x) = -12x^2 - 42x

    solving for f''(x) = 0 yields x=0 and x=-\frac{7}{2}
    so, the intervals for testing are (-\infty ,-\frac{7}{2}), (-\frac{7}{2}, 0),(0,+\infty)

    if x is in (-\infty ,-\frac{7}{2}), then f''(x) < 0

    if x is in (-\frac{7}{2}, 0), then f''(x) > 0

    if x is in (0,+\infty), then f''(x) < 0

    given that, when is the function concave up or down?
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