The tangent plane to the surface with equation = at the point (x, y, z) = (4, 1,67) has the equation z (write the appropriate function of x and y) The tangent plane to the surface with equation at the point where (x, y) = (1,0) has the equation z = (write the appropriate function of x and y) The tangent plane to the graph of = at the point where (x, y) = (2,2) has the equation z (write the appropriate function of x and y) z = x ln (y) + x³ y + 3 Z= - 3y + 3 3x + y + 12 X- BS f (x, y) = ln (4x² y+1) Po

Find the directions in which f increases and decreases most rapidly at point P. Then find the derivatives of f in these directions. f(x, y) = 3x? + 2xy+ 4y², P = (7,8) Direction of fastest increase is Direction of fastest decrease is Derivative in the direction of fastest increase is Derivative in the direction of fastest decrease is f(х, у) — х? у + е2хy sin(y), Р 3 (-3, 0) Direction of fastest increase is Direction of fastest decrease is Derivative in the direction of fastest increase is Derivative in the direction of fastest decrease is