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Math Help - Which of the following describes the behavior of y=(x+2)^(1/3(

  1. #1
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    Which of the following describes the behavior of y=(x+2)^(1/3(

    Which of the following describes the behavior of y=(x+2)^(1/3)

    a) cusp
    b) corner
    c) vertical tangent

    how do you prove it/figure it out?
    Last edited by mr fantastic; December 16th 2009 at 03:46 AM. Reason: Copied post title into main body of post.
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  2. #2
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    if you graph it out, its a vertical tangent.

    if you want to find what it is algebraically though, take the derivative and see where its undefined. the derivative is undefined at x = -2.

    now take the right and left hand limits of the derivative of (x+2)6(1/3) as x approaches -2. if you plug in -2 directly you are going to get 1/0 which tells you that it is +/- infinite. if you plug in numbers very close to -2, since the (x+2) is being squared (and then take the cube root), the denominator will always be positive so both limits approach +infinite. since this is the case, it must be a vertical tangent. graph the function out and see if this makes sense geometrically.
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  3. #3
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    Quote Originally Posted by craz View Post
    Which of the following describes the behavior of y=(x+2)^(1/3)

    a) cusp
    b) corner
    c) vertical tangent

    how do you prove it/figure it out?
    I assume you want to know the natue of the point (-2, 0). It's the same as the nature of the point (0, 0) on the curve y = x^{1/3}. With reference to that curve, note that:
    1. The domain is all real numbers.
    2. The curve is monotonically increasing.
    3. The derivative is undefined at x = 0.
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