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Math Help - How to do this (tangent line)

  1. #1
    Member Marconis's Avatar
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    How to do this (tangent line)

    I am beginning to study for my Calc 1 final by doing all of the old finals that are up on the math dept. page.

    One question is:

    If the line tangent to the graph of f (x) = x3 + 1 at the point (a, f (a)) passes
    through the origin, then a is:

    How am I to go about doing this? In all the practice I have done, and all the questions that have shown on my exam, a was given when it asked for a tangent line passing through a point (a,f(a)). So I don't know how to find a........
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  2. #2
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    a=0 since the origins coordinates are (0,0)
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  3. #3
    Member Marconis's Avatar
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    It's a MC question, and none of the answers are 0. That's why I am confused...
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  4. #4
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    What are the choices?
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  5. #5
    Member Marconis's Avatar
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    A) sqrt 3
    B) 1/sqrt 3
    C)  cbrt 2
    D) 1/cbrt 2
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  6. #6
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    I have no clue. I still think it is 0.
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  7. #7
    Member Marconis's Avatar
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    You and me both.
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  8. #8
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    What is the answer supposed to be?
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  9. #9
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    Nah, I don't think it's 0. I believe it is D.

    f(x) = x^3 + 1

    f'(x) = 3x^2

    If the line tangent to f(x) is in the form y = mx + b, we know b = 0 since it passes through the origin. So all we know is the slope of this line, m = 3x^2. So the equation of our tangent line is:

    y = (3x^2)x = 3x^3. We wish to find when this intersects the original function. So we equate them.

    3x^3 = x^3 + 1

    2x^3 = 1

    x^3 = \frac{1}{2}

    x = \frac{1}{2^{1/3}}

    So choice D it is.
    Last edited by elemental; December 1st 2010 at 07:39 PM. Reason: made it look better
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  10. #10
    Member Marconis's Avatar
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    Cool stuff. Thanks!

    I love how we never learned such a thing, and it was on a final in 08. Oh boy.
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  11. #11
    Member Marconis's Avatar
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    Nvm

    10char
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