Let f be a multivariable function defined by f(x, y) = x3y – x2y2 where x and y are real numbers

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.

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 any point on the y-axis.