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Finding critical points of a function z=f(x,y)

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Find all critical points of the function:

f (x,y) = x^3 + y^3 - 4x - 9y + 17

Classify the critical point as a relative minimum, relative maximum, or saddle point using the second derivative test.

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Solution Summary

In this exercise, a 3-dimensional function is plotted out and then the process of locating critical points is provided. It is determined whether they are minimums, maximums, or saddle points using an analysis of the first and second derivatives of the function.

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See attachment.

Find all critical points of the function:

f (x,y) = x^3 + y^3 - 4x - 9y + 17

Classify the critical point as a relative minimum, relative maximum, or saddle point using the second derivative test.
First we solve the gradient of f (x,y) = x^3 + y^3 - 4x - 9y + 17
This ...

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