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Math Help - continuous - differentiable question

  1. #1
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    continuous - differentiable question

    is this true?
    lets say that f and g are continuous on [a, b] and differentiable on (a, b).
    If f'(x)=g'(x) for all x in (a, b), then f and g differ by a constant.

    i think it false..
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  2. #2
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    let h(x)=f(x)-g(x), and h'(x)=f'(x)-g'(x)=0, thus h(x) is constant and the conclusion follows.
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  3. #3
    DBA
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    Why you think it is false?

    If f'(x)=g'(x) then both functions have at x the same slope. For example x=1.

    f'(1) = 3 then g'(x) = 3 --> this tells you that both graphs have a slope of 3 at x=3
    but the funtion itself can be different. Like f(1) = 2 and g(1) = 4, then the two curves would have the same slope at x=1 but are lying parallel to each other.

    The same for an maximum or minimum point. If f(1)=0 and g(1) =0 then both functions have an max or min at x=1 but the maximum/minimum value of f(x)could be at (1,3) and the other of g(x) could be at (1,4)

    The function values I used are just random examples.

    Thats how I understood it. Hope it helps.
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