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Given the level surface S defined by f(x, y, z) = x − y3 − 2z2...

Given the level surface S defined by f(x, y, z) = x − y3 − 2z2 = 2 and the point P0(−4, −2, 1).

Find the equation of the tangent plane to the surface S at the point P0.

Find the derivative of f at P0in the direction of r(t) =< 3, 6, −2 >

Find the direction and the value of the maximum rate of change greatest increase of f at P0;

(d) Find the parametric equations of the tangent line at P0 to the curve of intersection of S and 2x − 3y − z = -3.

Math   Calculus   
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