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Math Help - need help

  1. #1
    Newbie
    Joined
    Nov 2007
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    6

    need help

    Consider f(x)=x^{1/2}. Find all value(s), c, in the interval [0,1] such that the slope of the tangent line to the graph of f at c is parallel to the secant line through the point (0, f(0)) and (1, f(1)).


    \frac{1}{2x^{1/2}}
    and slope of (0. f(0)) and (1,f(1)) is 1
    This is all i can do, need help on this
    thx in advance
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  2. #2
    Super Member
    Joined
    Oct 2007
    From
    London / Cambridge
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    well you took the derivative correctly ad you know the required slop is equal to 1

     \frac{1}{2\sqrt{x}}=1

    just solve that equation.
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  3. #3
    Super Member

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    May 2006
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    Lexington, MA (USA)
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    Hello, Bryan!

    You're almost there . . .


    Consider f(x)\:=\:x^{\frac{1}{2}}.
    Find all value(s), c, in the interval [0,1] such that the slope of the tangent line
    to the graph of f at c is parallel to the secant line through: (0,\,f(0)) and (1, f(1)).


    The slope of the tangent is: . \frac{1}{2x^{\frac{1}{2}}} . . . . Yes!

    . . and slope of (0, f(0)) and (1, f(1)) is 1 . . . . Right!

    So when is: . \frac{1}{2\sqrt{x}} equal to 1?

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