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Thread: root function analysis

  1. #1
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    root function analysis

    Here is the function $\displaystyle y=x*sqrt[a+b*x^2]$
    the tangent equation of the function at $\displaystyle x=sqrt[5]$
    is $\displaystyle x+2y=5*sqrt[5]$

    A. Find a and b.
    B. Find the function definition range.
    C. Find the minimum & maximum points.

    We tried to derive the function but we didn't succeed.
    Please help us to finish the question.
    Thanks.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by natanson.meital View Post
    Here is the function $\displaystyle y=x*sqrt[a+b*x^2]$
    the tangent equation of the function at $\displaystyle x=sqrt[5]$
    is $\displaystyle x+2y=5*sqrt[5]$

    A. Find a and b.
    B. Find the function definition range.
    C. Find the minimum & maximum points.

    We tried to derive the function but we didn't succeed.
    Please help us to finish the question.
    Thanks.
    When $\displaystyle x=\sqrt{5}$ we have from the original equation:

    $\displaystyle y=\sqrt{5} \sqrt{a+5b}$

    and from the tangent equation:

    $\displaystyle y=2 \sqrt{5}$

    so:

    $\displaystyle a+5b= 4$

    You obtain the second equation that you need by equating derivatives of the
    original equation and tangent at $\displaystyle x=\sqrt{5}$, which I will leave to you.

    RonL
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