Math, asked by sumitverma0108, 1 year ago

Find the slope of the tangent at (3, 1, 1) to the curve of intersection of x = 3 and z= x²y - 3xy² + 1

Answers

Answered by kvnmurty
4
The plane  x = 3,  and the 3-d surface (solid) z = x² y - 3 x y² + 1  intersect in a 2-d curve :   z = 3² y - 3 * 3 y² + 1
       ie.,  z = 9 y - 9 y² + 1
       ie.,   (z - 13/4)  = - 9 (y - 1/2)² 
  It is a parabola.
        slope of the tangent is given by dz/dy.
         dz/dy = 9 - 18 y  = 9 - 18 * 1  = - 9      at  (3, 1, 1).


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