A+ Answers

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

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.