multivariate function – min, max, eq of tan plane,normal line, second derivative test for extreme values

Let f be a multivariable function defined by f(x, y) = x³y – x²y² where x and y are real numbers. Choose the same point to use as you work to complete parts A through D of the task.

A.    Explain how to find the direction of maximum increase for f at your chosen point, showing all required work.

B.    Explain how to find the direction of maximum decrease for f at your chosen point, showing all required work.

C.    Explain how to find the equation of the tangent plane to f at your chosen point, showing all required work.

D.    Explain how to find the equation of the normal line to f at your chosen point, showing all required work.

E.    Demonstrate that the second derivative test for local extreme values of f is inconclusive for all points on the y-axis.