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Math Help - Domain of Derivative and Integral

  1. #1
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    Domain of Derivative and Integral

    If the functions f and g are defined for all real numbers and f is an anti-derivative of g, which of the following statements is NOT necessarily
    correct?

    1. If g(x) > 0 for all x, then a is increasing

    2. if g(a) = 0 then the graph of a has a horizontal tangent at x = a

    3. If f(x) = 0 for all x, then g(x) = 0 for all x

    4. if g(x) = 0 for all x, then f(x) = 0 for all x - ANSWER - Why?

    5. f is continuous for all x
    Last edited by Jason76; August 26th 2013 at 07:45 PM.
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  2. #2
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    Re: Domain of Derivative and Integral

    For number 4, if the derivative is zero, the function is constant - not necessarily zero.

    - Hollywood
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    Re: Domain of Derivative and Integral

    Quote Originally Posted by hollywood View Post
    For number 4, if the derivative is zero, the function is constant - not necessarily zero.

    - Hollywood
    Thanks.
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    Re: Domain of Derivative and Integral

    1. What is a. If g(x) > 0 for all x then g(x) is increasing.
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  5. #5
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    Re: Domain of Derivative and Integral

    I assume he means 1. If g(x) > 0 for all x then f is increasing.

    - Hollywood
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