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