RIJEÃ…Â ENI ZADACI IZ MATEMATIKE
RIJEÃ…Â ENI ZADACI IZ MATEMATIKE
RIJEÃ…Â ENI ZADACI IZ MATEMATIKE
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51. Izračunajte ekstreme funkcijef(x, y) = e x2 +y 2 −4xRješenje:f x = e x2 +y 2 −4x · (2x − 4)e x2 +y 2 −4x · (2x − 4) = 02x − 4 = 0x = 2f y = e x2 +y 2 −4x · 2ye x2 +y 2 −4x · 2y = 02y = 0y = 0D 1 = f xxf xx = e x2 +y 2 −4x · (2x − 4) 2 + e x2 +y 2 −4x · 2f xx = e x2 +y 2 −4x [ (2x − 4) 2 + 2 ]f xx = 2e −4D 1 = 2e −4 > 0D 2 = f xx f yy − f 2 xyf yy = e x2 +y 2 −4x · 4y 2 + e x2 +y 2 −4x · 2f yy = e x2 +y 2 −4x (4y 2 + 2)f yy = 2e −449
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