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Engineering Calculus Notes 377

Engineering Calculus Notes 377 - 365 3.8 LOCAL EXTREMA g...

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3.8. LOCAL EXTREMA 365 g has a strict minimum at the origin: g ( −→ x ) > 0 for all −→ x negationslash = −→ 0 , and h has saddle behavior: its restriction to the x -axis has a minimum at the origin, while its restriction to the line y = x has a maximum at the origin. As an example, consider the function f ( x,y ) = 5 x 2 + 6 xy + 5 y 2 8 x 8 y. We calculate the first partials f x ( x,y ) = 10 x + 6 y 8 f y ( x,y ) = 6 x + 10 y 8 and set both equal to zero to find the critical points:
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