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Math Help - [SOLVED] Gradient of a Tangent.

  1. #1
    Member Awsom Guy's Avatar
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    [SOLVED] Gradient of a Tangent.

    I think this belongs here, hopefully here....

    What is the gradient of the tangent to the graph of f(x)=sqrt(x) at the point where x=9.
    I think the answer should be 0.
    But I need the answer confirmed.
    Thanks.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by Awsom Guy View Post
    I think this belongs here, hopefully here....

    What is the gradient of the tangent to the graph of f(x)=sqrt(x) at the point where x=9.
    I think the answer should be 0.
    But I need the answer confirmed.
    Thanks.
    HI

    nope , its not 0

    f'(x)=\frac{1}{2\sqrt{x}}

    =\frac{1}{2\sqrt{9}}

     <br />
=\frac{1}{6}<br />
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  3. #3
    Member Awsom Guy's Avatar
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    ?

    where's the 2 from.
    Please explain.
    Thanks
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  4. #4
    Member Awsom Guy's Avatar
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    hold on..

    i think im getting it but I cant find out how to get the inverse 1/ bit.
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  5. #5
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    Quote Originally Posted by Awsom Guy View Post
    i think im getting it but I cant find out how to get the inverse 1/ bit.
    The power rule for differentiation is: \frac{d}{dx} ax^n = nax^{n-1} where a and n are constants.

    For this case: f(x) = \sqrt{x} so a=1 and n = \frac{1}{2}

    Thus: f'(x) = \frac{1}{2} x^{\frac{-1}{2}} = \frac{1}{2\sqrt{x}}
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  6. #6
    Member Awsom Guy's Avatar
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    thanks

    thanks I get that.
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