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Math Help - Tangent and parallel lines

  1. #1
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    Tangent and parallel lines

    Find all lines that are tangent to the curve y = x^3 and are also parallel to the line 3x - y = 5

    Any help will be appreciated!
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  2. #2
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    Quote Originally Posted by hasanbalkan View Post
    Find all lines that are tangent to the curve y = x^3 and are also parallel to the line 3x - y = 5

    Any help will be appreciated!
    Firstly,
    y=x^3
    y'=3x^2

    The lines must be parallel to 3x-y = 5, y=3x-5. So their slope must be m=3.

    Let our line be y=m\cdot x + C, m is the slope and C is a constant. As m=3 it'll become y=3x + C

    At the tangent point, the line must satisfy m=3=3x^2.
    3x^2 = 3
    x^2=1
    x= \pm 1

    So the line passes the points (-1,f(-1)) and (1,f(1)).
    (-1,-1), (1,1)

    The line is y=3x + C
    And it makes C=2 for (-1,1)
    and C=-2 for (-1,1)

    The lines are then
    y=3x + 2 and y=3x - 2

    bu arada, türk müsün? =)
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