Question

срочно профильная математика!!
какое нибудь из трёх номеров!! помогите!

Answer 1

Ответ:

11.

$z = \cos(3x - {x}^{2} {y}^{2} )$

$z'_y = - \sin(3 x - {x}^{2} {y}^{2} ) \times ( - 2 {x}^{2} y) = \\ = 2 {x}^{2} y \sin(3x - {x}^{2} {y}^{2} )$

$z''_{yy} = (2 {x}^{2} y)'_y \times \sin(3x - {x}^{2} {y}^{2} ) + ( \sin(3x - {x}^{2} {y}^{2} ) )'_y \times 2 {x}^{2} y = \\ = 2 {x}^{2} \sin(3x - {x}^{2} {y}^{2} ) + \cos(3x - {x}^{2} {y}^{2} ) \times ( - 2 {x}^{2} y) \times 2 {x}^{2} y = \\ = 2 {x}^{2} \sin(3x - {x}^{2} {y}^{2} ) - 4 {x}^{4} {y}^{2} \cos(3x - {x}^{2} {y}^{2} )$

12.

$f(xy) = 10 + 22x + 12y - 4 {x}^{2} - 5xy - 2 {y}^{2}$

$f'_x = 22 - 8x - 5y \\ f'_y = 12 - 5x - 4y$

$f'_x = 0 \\ f'_y = 0 \\ \\ 22 - 8x - 5y = 0 \: \: \: | \times 4 \\ 12 - 5x - 4y = 0 \: \: \: | \times 5 \\ \\ 88 - 32x - 20y = 0 \\ 60 - 25x - 20y = 0 \\ \\ (1) - (2) \\ \\ 28 - 7x = 0 \\ x = 4 \\ \\ y = \frac{22 - 8x}{5} = - \frac{10}{5} = - 2$

Ответ: М(4; -2) - экстремум