The Jacobian Matrix of the System $x ^ { \prime } = x ^ { 3 } - y ^ { 2 } + 4 , y ^ { \prime } = 5 x$

question 12

Multiple Choice

The Jacobian matrix of the system $x ^ { \prime } = x ^ { 3 } - y ^ { 2 } + 4 , y ^ { \prime } = 5 x$ at the critical point $( 0,2 )$

• A) \(A = \left[ \begin{array} { c c }
• 0 & - 4 \\
• 5 & 0
• \end{array} \right]\)
• B) \(A = \left[ \begin{array} { l l }
• 0 & 4 \\
• 5 & 0
• \end{array} \right]\)
• C) \(A = \left[ \begin{array} { r r }
• 3 x ^ { 2 } & 2 y \\
• 5 & 0
• \end{array} \right]\)
• D) \(A = \left[ \begin{array} { r r }
• 3 x ^ { 2 } & - 2 y \\
• 5 & 0
• \end{array} \right]\)
• E) \(A = \left[ \begin{array} { r r }
• 3 x ^ { 2 } & - 2 y \\
• 0 & 5
• \end{array} \right]\)

Recognize the significance of critical events during the prenatal development period, including organ formation and system maturation.

Illustrate the embryonic and extraembryonic structures contributing to early human development.

Understand the dynamics of demand forecasting for seasonal products.

Analyze cost components in sales and operations planning.

---

Definitions:

Private Value

Represents the worth or value of a good or service to an individual consumer, which may differ from its market price or cost to others.

Antibiotic-Resistant Diseases

Conditions caused by bacteria that have evolved to survive treatments with antibiotics previously effective against them.

Socially Optimal Quantity

The level of production of goods and services that maximizes societal welfare, taking into account external costs and benefits.

Antibiotics

Medications used to treat bacterial infections by either killing bacteria or inhibiting their growth.