Tìm cực trị của hàm\[{\rm{z = }}{{\rm{x}}^{\rm{2}}}{\rm{ + 3}}{{\rm{y}}^{\rm{2}}}{\rm{ + x}} - {\rm{y}}\]với điều kiện x + y = 1. Khẳng định nào sau đây đúng?

A. \[{\rm{y = }}{{\rm{C}}_{\rm{1}}}{{\rm{e}}^{ - {\rm{x}}}}{\rm{ + }}{{\rm{C}}_{\rm{2}}}{{\rm{e}}^{{\rm{3x}}}}\]

B. \[{\rm{y = }}{{\rm{C}}_{\rm{1}}}{{\rm{e}}^{\rm{x}}}{\rm{ + }}{{\rm{C}}_{\rm{2}}}{{\rm{e}}^{{\rm{3x}}}}\]

C. \[{\rm{y = }}{{\rm{C}}_{\rm{1}}}{{\rm{e}}^{ - {\rm{x}}}}{\rm{ + }}{{\rm{C}}_{\rm{2}}}{{\rm{e}}^{ - {\rm{3x}}}}\]

D. \[{\rm{y = }}{{\rm{C}}_{\rm{1}}}{{\rm{e}}^{{\rm{2x}}}}{\rm{ + }}{{\rm{C}}_{\rm{2}}}{{\rm{e}}^{{\rm{3x}}}}\]

A. x = 1, y = 1

B. x = 0, y = 0

C. x = 1, y = 0

D. x = 0, y = 1

A. 3

B. 2

C. 6

D. 9.ln3

A. \[{\rm{y = C}}\left( {\rm{x}} \right){\rm{sinx}}\]

B. \[{\rm{y = }}\frac{{{\rm{C(x)}}}}{{{\rm{sinx}}}}\]

C. \[{\rm{y = C(x) + sinx}}\]

D. \[{\rm{y = C(x)}} - {\rm{sinx}}\]

A. M = 8

B. M = 9

C. M = 10

D. M = 7

A. \[\frac{{\partial {\rm{z}}}}{{\partial {\rm{x}}}} = \frac{1}{{\sqrt {{{\rm{x}}^{\rm{2}}}{\rm{ + }}{{\rm{y}}^{\rm{2}}}} }}\]

B. \[\frac{{\partial {\rm{z}}}}{{\partial {\rm{x}}}} = \frac{{ - 1}}{{\sqrt {{{\rm{x}}^{\rm{2}}}{\rm{ + }}{{\rm{y}}^{\rm{2}}}} }}\]

C. \[\frac{{\partial {\rm{z}}}}{{\partial {\rm{x}}}} = \frac{{2x}}{{\sqrt {{{\rm{x}}^{\rm{2}}}{\rm{ + }}{{\rm{y}}^{\rm{2}}}} }}\]

D. \[\frac{{\partial {\rm{z}}}}{{\partial {\rm{x}}}} = \frac{x}{{\sqrt {{{\rm{x}}^{\rm{2}}}{\rm{ + }}{{\rm{y}}^{\rm{2}}}} }}\]

A. \[\frac{{32{\rm{\pi }}}}{5}\]

B. \[\frac{{64{\rm{\pi }}}}{5}\]

C. \(8\pi \)