Find Values of X, Y, and λ That Satisfy the System

question 11

Short Answer

Find values of x, y, and λ that satisfy the system. These systems arise in certain optimization problems in calculus, and λ is called a Lagrange multiplier.
​ $$\left\{ \begin{array} { r } 4 x - 4 x \lambda = 0 \\- 2 y + \lambda = 0 \\y - x ^ { 2 } = 0\end{array} \right.$$ ​

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Definitions:

Ego

In psychoanalysis, the part of the psyche that mediates between the conscious, the unconscious, and the external world.

Implicit Selves

The unconscious aspects of the self, including attitudes and beliefs that influence behavior without conscious awareness.

Explicit Selves

The aspects of an individual's self-concept that are consciously recognized and expressed.

Independent Self

A concept in psychology referring to individuals who perceive themselves as distinct and autonomous, with an emphasis on personal goals and self-reliance.