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Math Help - critical points and local extrema

  1. #1
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    critical points and local extrema

    find the critical points and classify local extrema.

    f(x)= 2-3x/2+x
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  2. #2
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    Quote Originally Posted by eayettey View Post
    find the critical points and classify local extrema.

    f(x)= 2-3x/2+x

    Is the function

    f(x)= 2-\frac{3x}{2}+x

    or

    f(x)= \frac{2-3x}{2+x}

    ??
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  3. #3
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    critical points and local extrema

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  4. #4
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    Thanks for clearing that up.

    If you divide the function as suggested then f(x) will be.

    <br />
\frac{2-3x}{2+x} = \frac{4}{2+x}-3

    so

    f(x) = \frac{4}{2+x}-3

    This suggests a vertical aymptote at x = -2 and a horizontal aymptote at y = -3.

    To find a y-intercept make x = 0

    f(0) = \frac{4}{2+0}-3 = 2-3 = -1

    To find a x-intercept make y = 0

    0 = \frac{4}{2+x}-3

    quotient rule

    3(2+x) = 4

    x = \frac{-2}{3}

    To find any maxima or minima you should use the
    quotient rule , set your derivative equal to zero and solve for x.

    quotient rule is, if

    y = \frac{u}{v}

    then

    y' = \frac{v\times u'-u\times v'}{v^2}

    I hope this helps some!
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  5. #5
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    Quote Originally Posted by eayettey View Post
    This is a rectangular hyperbola. This fact is made obvious in post #4. So it has no critical points.
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