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Math Help - Need help finding relative extrema

  1. #1
    bmh
    bmh is offline
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    Need help finding relative extrema

    I need help finding the relative extrema for : f(x) = square root of x^2+1

    , by using the first and second derivative tests
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by bmh View Post
    I need help finding the relative extrema for : f(x) = square root of x^2+1

    , by using the first and second derivative tests
    f(x)=\sqrt{x^2 + 1}
    then,
    f'(x)=\frac{x}{\sqrt{x^2 + 1}}
    then, get the critical point,
    f'(x)=x=0
    so,
    x=0
    then,
    f''(x)=\frac{\sqrt{x^2 + 1} - x\frac{x}{\sqrt{x^2 + 1}}}{x^2 + 1}
    if you simplify this, you will get
    f''(x)= \frac{1}{(\sqrt{x^2 + 1})(x^2 + 1)}
    which is always positive, therefore the function assumes a minimum point at x=0. so by first and second derivative test, the relative minimum point of
    f(x)=\sqrt{x^2 + 1}
    is at (0,1)..
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