bai tap chuong 3

CỰC TRỊ TỰ DO, CỰC TRỊ CÓ ĐIỀU KIỆN, GTLN-GTNN Tính cực trị hàm sau: a) f ( x, y ) = x + y − xy b) f ( x, y ) = − ( x + y ) c) f ( x, y ) = x + y − xy + x − y d) f ( x, y ) = y x − y − x + y e) f ( x, y ) = x + y − x − xy − y f) f ( x, y, z ) = x + y + z − x + y − z Tính cực trị có diều kiện hàm sau: a) f ( x, y ) = x + y, x2 + y =  x2 + y + z − = b) f ( x, y, z ) = xyz ,  x + y + z =  Tìm GTLN, GTNN hàm sau: 2 2 a) f ( x, y ) = x + y − 12 x − 16 y, D : x + y ≤ 25 2 b) f ( x, y ) = x + y − xy + x + y , D : x ≤ 0, y ≤ 0, x + y ≥ −3 Đáp án: a) CT (1,1), fCT = -1 b) CT (xo,yo): xo - yo+1 = 0, fCT = c) CĐ (0,0), fCĐ = d) CĐ (4,4), fCĐ = 12 e) CT (-1,-1),(1,1), fCT = -2 f) CT (2,-3,1), fCT = -14 a) CĐ (1,2), CT (-1,-2)… 1 −2 −2 −2 , ),( , , ),( , b) CT ( , 6 6 6 CĐ (− , − , ),(− , , − ),( 6 6 6 a) GTNN (3,4), fmin = -75, GTLN (-3,-4), fmax = 125 b) GTNN (-1,1), fmin = -1, 1 , ) 6 1 ,− ,− ) 6 GTLN (-3,0), (0,-3), fmax = ...GTLN ( -3, 0), (0, -3) , fmax =