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Math Help - Question from Calculus Mid

  1. #1
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    Question from Calculus Mid

    Given f(x) and g(x), where f'(x) > g'(x) at all points, how many times can the two funtions intersect?
    (i) Exactly Once
    (ii) More than Once
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  2. #2
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    Re: Question from Calculus Mid

    Quote Originally Posted by sk9190 View Post
    Given f(x) and g(x), where f'(x) > g'(x) at all points, how many times can the two funtions intersect?
    (i) Exactly Once
    (ii) More than Once
    Consider how many x-intercepts a graph of the function y = f(x) - g(x) can have ....
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    Re: Question from Calculus Mid

    I'm not sure I follow. Can you elaborate?
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    Re: Question from Calculus Mid

    Quote Originally Posted by mr fantastic View Post
    Consider how many x-intercepts a graph of the function y = f(x) - g(x) can have ....
    Well, if y = f(x) - g(x), what do you know about dy/dx and what implications does that have on the number of x-intercepts that y has ....?
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    Re: Question from Calculus Mid

    I'm thinking the answer is Exactly once and all the possible functions for f and g that I can think of support this, but I don't understand the basic principle as to why
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    Re: Question from Calculus Mid

    Quote Originally Posted by sk9190 View Post
    I'm thinking the answer is Exactly once and all the possible functions for f and g that I can think of support this, but I don't understand the basic principle as to why
    Then you need to reflect on what I posted for more than just a handful of minutes.
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    Re: Question from Calculus Mid

    Alright, I'm giving it 10 minutes, but if I can't figure it out then can you just spell it out for me? =P
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    Re: Question from Calculus Mid

    Quote Originally Posted by sk9190 View Post
    Alright, I'm giving it 10 minutes, but if I can't figure it out then can you just spell it out for me? =P
    You know that dy/dx = f'(x) - g'(x) > 0 for all values of x. Now think about what dy/dx > 0 means in terms of the behaviour of the graph.
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