Use the Method of Lagrange Multipliers to Find Points on the Surface

question 229

Essay

Use the method of Lagrange multipliers to find points on the surface of $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 3$ where the function $f ( x , y , z ) = x + y + z$ has
(a) a minimum
(b) a maximum.

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Definitions:

Following

In the context of reactions, "following" generally refers to the sequence or order in which reactants undergo transformations in a chemical process.

Bond Dipole Moment

A measure of the inequality in the electron distribution between two atoms in a bond, leading to a polar molecule if present across the molecule.

Methanol

The simplest alcohol, with the formula CH3OH, used as a solvent, antifreeze, fuel, and as a precursor to other chemicals.

C-O Bond

The covalent bond formed between a carbon and an oxygen atom, a fundamental bond in organic chemistry.