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

question 83

Short Answer

Determine the minimum value of f(x, y) = $x ^ { 2 }$ - xy + 2 $y ^ { 2 }$ + 4 subject to the constraint $x - y - 1 = 0$ Enter your answer exactly as just a, b where a is the minimum and b is the Lagrange multiplier, using integers or reduced fractions of form $\frac { \mathrm { c } } { \mathrm { d } }$ (no words or units).

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Definitions:

Altitude

The height of an object or point in relation to sea level or ground level.

Oxyhemoglobin

The form of hemoglobin bound to oxygen, responsible for transporting oxygen from the lungs to the body's tissues.

Deoxyhemoglobin

Hemoglobin without oxygen bound to it.

Carboxyhemoglobin

A complex of carbon monoxide and hemoglobin, formed by the binding of carbon monoxide to hemoglobin, which impairs oxygen delivery.