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Math Help - One more Calculus Problem

  1. #1
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    One more Calculus Problem

    4. Let f(x) and g(x) be the differentiable functions graphed here. At x=c, the vertical distance between these curves is the greatest. Is there anything special about the tangents to the two curves at x=c? Give reasons for your answers. f(x) is the line that is concave up, and g(x) is the line that is concave down.

    I am in the first semester of calculus, so this would have to apply to that.... but I have no clue where to start on this one :P. So help would be nice.
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  2. #2
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    Forgot to put the graph here.
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Prophet View Post
    4. Let f(x) and g(x) be the differentiable functions graphed here. At x=c, the vertical distance between these curves is the greatest. Is there anything special about the tangents to the two curves at x=c? Give reasons for your answers. f(x) is the line that is concave up, and g(x) is the line that is concave down.

    I am in the first semester of calculus, so this would have to apply to that.... but I have no clue where to start on this one :P. So help would be nice.
    the vertical distance between the functions at any value of x is given by f(x) - g(x). define a new function, h(x), to be this distance. thus we have:

    h(x) = f(x) - g(x)

    now we want to maximize h. so we find its derivative and set it equal to zero, thus we have:

    h'(x) = f'(x) - g'(x) = 0

    what can we say about f'(x) and g'(x)? which are the slopes of the tangent lines of f(x) and g(x) respectively
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