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Maximum, minimum, saddle points

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Please see the attached file.

Find the local maximum and minimum values and saddle point(s) of the function.

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Solution Summary

This shows how to find local maximum and minimum values and saddle points for a given function.

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#11 f(x, y) = 2x3 + xy2 + 5x2 + y2 + 5

f'(x) = 6x2 + y2 + 10x = 0
f'(y) = 2xy + 2y = 0, which gives y(x + 1) = 0m or y = -(x + 1)
Plugging this in the first equation,
6x2 + (x + 1)2 + 10x = 0
Or 6x2 + x2 + 1 + 2x + 10x = 0
Or 7x2 + 12x + ...

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