MAT1322-3X Solution to Final Examination Summer 2017
6. (4 marks)Suppose a function z= f(x, y) is defined implicitly by the equation F(x, y, zwhere F(x, y, z) = x3–y2z+ xyz(a) (1 mark) Find the partial derivative zxand zyat the point (1, 2, −1).(b) (1 mark) Find the equation of the tangent plane of the graph of this equation at the point (1, 2, −1).(c) (1 mark) Find the directional derivative of this function at point (1, 2, −1) in the direction of the vector u= 34,55) = 3, 3. .