calculus

How do I find the x values at which the tangents to the graphs f(x)=2x^2 and g(x)=x^3 have the same slope?

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  1. f'(x) = 4 x
    g'(x) = 3 x^2
    when does 4x = 3 x^2 ?
    3 x^2 - 4 x = 0
    x (3x -4) = 0
    x = 0 and x = 4/3

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  2. Assuming you are looking for the same value of x at which both tangents are parallel.

    Take derivative of each, equate and solve for x.

    f'(x)=4x
    g'(x)=3x²
    Equate and solve to get
    x=0 or x=4/3

    See:
    http://img855.imageshack.us/i/1299374046.png/

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