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Math Help - strictly concave up function

  1. #1
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    strictly concave up function

    suppose that f : R-->R is strictly concave up, strictly increasing function with a zero t satisfying a<t< b
    Which of the following are true
    1.f(b)<0
    2.f(b)=0
    3.f(b)>0
    4.f(a)<0
    5.f(a)=0
    6.f(a)>0
    7.impossible to determine

    can someone help me with this
    Last edited by dat1611; August 8th 2010 at 07:44 AM.
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  2. #2
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    I would feel better about answering if you had shown some attempt yourself!

    Consider the function f(x)= x^2- 1 with
    i) a= 0, b= 2
    ii) a= -2, b= 0
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    i don't understand what i'm supposed to do
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    Quote Originally Posted by dat1611 View Post
    suppose that f : R-->R is strictly concave up, strictly increasing function with a zero t satisfying a<t< b
    Which of the following are true
    1.f(b)<0
    2.f(b)=0
    3.f(b)>0
    4.f(a)<0
    5.f(a)=0
    6.f(a)>0
    7.impossible to determine
    Do you know what a strictly increasing function means?
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  5. #5
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    upward sloping i think not sure what zero t means
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  6. #6
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    Quote Originally Posted by dat1611 View Post
    upward sloping i think not sure what zero t means
    f(x) is a strictly increasing function. that tells you that if a < t < b , then f(a) < f(t) < f(b)

    "zero t" means f(t) = 0
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  7. #7
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    ok so...
    1.f(b)<0 false
    2.f(b)=0 false
    3.f(b)>0 true
    4.f(a)<0 true
    5.f(a)=0 false
    6.f(a)>0 false
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