Please show all the work required to solve the multivariable calculus questions. Please sketch the functions so I can see conceptually what the...

Please show all the work required to solve the multivariable calculus questions. Please sketch the functions so I can see conceptually what the solutions mean. (Either by hand or using mathematica/engineering software)

(max/min, gradient, and tangent planes)

o give the direction of max increase of f(x,y,z) = ln (x2 +y2 - 1) + y + 6z at the point P(1,1,0)

o in what direction is the (directional) derivative of f(x,y) = xy + y2 at P(3,2) equal to zero?

o give the equation of the plane tangent to the ellipsoid x2 + 2y2 + 3z2 = 20 at the point P(3,2,1)