Finding Local Extrema Find all the local maxima, local minima, and saddle points of the functions in Exercises 1-30. 1. f(x,y)=x2+xy+y2+3x−3y+4 2. f(x,y)=2xy−5x2−2y2+4x+4y−4 3. f(x,y)=x2+xy+3x+2y+5 4. f(x,y)=5xy−7x2+3x−6y+2 5. f(x,y)=2xy−x2−2y2+3x+4 6. f(x,y)=x2−4xy+y2+6y+2 7. f(x,y)=2x2+3xy+4y2−5x+2y 8. f(x,y)=x2−2xy+2y2−2x+2y+1 9. f(x,y)=x2−y2−2x+4y+6 10.

Solution Given function is find all the first-order partial derivatives:

Resuelto Finding Local Extrema Find all the local maxima,

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Pregunta: Finding Local Extrema Find all the local maxima, local minima, and saddle points of the functions in Exercises 1-30. 1. f(x,y)=x2+xy+y2+3x−3y+4 2. f(x,y)=2xy−5x2−2y2+4x+4y−4 3. f(x,y)=x2+xy+3x+2y+5 4. f(x,y)=5xy−7x2+3x−6y+2 5. f(x,y)=2xy−x2−2y2+3x+4 6. f(x,y)=x2−4xy+y2+6y+2 7. f(x,y)=2x2+3xy+4y2−5x+2y 8. f(x,y)=x2−2xy+2y2−2x+2y+1 9. f(x,y)=x2−y2−2x+4y+6 10.

can you solve question 20 for me

Muestra el texto de la transcripción de la imagen
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Solución
Paso 1
Solution
Given function is
$\begin{aligned} f (x) & = x^{4} + y^{4} + 4 x y \end{aligned}$
find all the first-order partial derivatives:
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Paso 2
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Paso 3
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Respuesta
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Texto de la transcripción de la imagen:

Finding Local Extrema Find all the local maxima, local minima, and saddle points of the functions in Exercises 1-30. 1.

f (x, y) = x^{2} + x y + y^{2} + 3 x - 3 y + 4

f (x, y) = 2 x y - 5 x^{2} - 2 y^{2} + 4 x + 4 y - 4

f (x, y) = x^{2} + x y + 3 x + 2 y + 5

f (x, y) = 5 x y - 7 x^{2} + 3 x - 6 y + 2

f (x, y) = 2 x y - x^{2} - 2 y^{2} + 3 x + 4

f (x, y) = x^{2} - 4 x y + y^{2} + 6 y + 2

f (x, y) = 2 x^{2} + 3 x y + 4 y^{2} - 5 x + 2 y

f (x, y) = x^{2} - 2 x y + 2 y^{2} - 2 x + 2 y + 1

f (x, y) = x^{2} - y^{2} - 2 x + 4 y + 6

10.

f (x, y) = x^{2} + 2 x y

11.

f (x, y) = 56 x^{2} - 8 y^{2} - 16 x - 31 + 1 - 8 x

12.

f (x, y) = 1 - 3 x^{2} + y^{2}

13.

f (x, y) = x^{3} - y^{3} - 2 x y + 6

14.

f (x, y) = x^{3} + 3 x y + y^{3}

15.

f (x, y) = 6 x^{2} - 2 x^{3} + 3 y^{2} + 6 x y

16.

f (x, y) = x^{3} + y^{3} + 3 x^{2} - 3 y^{2} - 8

17.

f (x, y) = x^{3} + 3 x y^{2} - 15 x + y^{3} - 15 y

18.

f (x, y) = 2 x^{3} + 2 y^{3} - 9 x^{2} + 3 y^{2} - 12 y

19.

f (x, y) = 4 x y - x^{4} - y^{4}

20.

f (x, y) = x^{4} + y^{4} + 4 x y