Determine the Minimum of F(x, Y) = $x ^ { 2 }$

question 8

Short Answer

Determine the minimum of f(x, y) = $x ^ { 2 }$ + 2 $y ^ { 2 }$ subject to the constraint x - 2y + 3 = 0.
Enter your answer exactly as just a, b where a is the minimum and b is the Lagrange multiplier, both as integers (no labels).

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Definitions:

IUPAC

The International Union of Pure and Applied Chemistry, an organization that sets standards for chemical nomenclature, terminology, and measurements.

Acceptable Name

A term used to describe a name that is officially recognized and conforms to the standards set by a governing body, such as in chemistry or taxonomy.

Compound

A chemical entity consisting of a combination of elements in a specific ratio, forming a substance with unique properties.

Acceptable Name

A name that meets the standard nomenclature rules set by IUPAC or other governing bodies, suitable for use in scientific contexts.