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Math Help - rate of change with a elliptic paraboloid

  1. #1
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    rate of change with a elliptic paraboloid

    Can someone help me solve this?

    A point moves along the intersection of the elliptic paraboloid z=x^2+3y^2 and the plane x=2. At what rate is z changing with y when the point is at (2,1,7)?
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  2. #2
    Senior Member AllanCuz's Avatar
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    Quote Originally Posted by mike21 View Post
    Can someone help me solve this?

    A point moves along the intersection of the elliptic paraboloid z=x^2+3y^2 and the plane x=2. At what rate is z changing with y when the point is at (2,1,7)?
    The rate of change is simply the derivative!

    The question asks for,

     \frac{ \partial z}{ \partial y }

    Which means we want the partial derivative with respect to y leaving x constant.

    If  z = x^2+3y^2 then  \frac{ \partial z}{ \partial y } = 6y

    Sub in your given point and you have your answer.
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