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Math Help - parametric curves

  1. #1
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    parametric curves

    x=t^2
    y=t^3-3t

    a) Show that C has two tangents at the point (3,0) and find their equation.
    b) Find the point on C where the tangent is horizontal or vertical.
    c) Determine where the curve is concave upward or downward?

    I was able to do part a and b, but I'm stuck on part c. How do you find the second derivative of this curve?
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  2. #2
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    Quote Originally Posted by cityismine View Post
    x=t^2
    y=t^3-3t

    a) Show that C has two tangents at the point (3,0) and find their equation.
    b) Find the point on C where the tangent is horizontal or vertical.
    c) Determine where the curve is concave upward or downward?

    I was able to do part a and b, but I'm stuck on part c. How do you find the second derivative of this curve?
    \frac{d^2 y}{d x^2} = \frac{d}{dx} \left[ \frac{dy}{dx}\right] = \frac{d}{dt} \left[ \frac{dy}{dx}\right] \cdot \frac{dt}{dx} \, ......
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  3. #3
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    That's the formula I'm having trouble understanding. But I googled some examples and I think I get it now. It's the derivative of the 1st derivative divided by the denominator of the first derivative, right?
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  4. #4
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    Quote Originally Posted by cityismine and edited (in red) by Mr F View Post
    That's the formula I'm having trouble understanding. But I googled some examples and I think I get it now. It's the derivative with respect to t of dy/dx divided by dx/dt, right?
    Right.
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