Let f be a multivariable function

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Introduction:

 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.

 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.


 

    • 7 years ago
    Let f be a multivariable function
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