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Tangent Plane

  1. Nov 5, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the points on the graph of z=(x^2)(e^y) at which the tangent plane is parallel to 5x-2y-.5z=0


    2. Relevant equations
    An equation of the tangent plane to z=f(x,y) at (a,b) is:
    z = f(a,b) + fx(a,b)(x-a) + fy(a,b)(y-b)


    3. The attempt at a solution
    Partial derivatives of function f(x,y)
    fx(x,y) = 2xe^y => fx(a,b) = 2ae^b
    fy(x,y) = (x^2)(e^y) => fy(a,b) = (a^2)(e^b)
     
  2. jcsd
  3. Nov 6, 2009 #2

    lanedance

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    Homework Helper

    ideas from here? you could check when the plane normal vectors are parallel, or alternatively check when the directions of both the partial derivatives are perpindicular to the plane normal

    you can also do this with graidents, but it amounts to a similar thing
     
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