Let f be a multivariable function defined by f(x, y) = x^3y – x^2y^2 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.
Requirements:
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.