Let $h ( x , y , z ) = x ^ { 2 } - 2 x \sin y + z$

question 75

Essay

Let $h ( x , y , z ) = x ^ { 2 } - 2 x \sin y + z$ .Let $f ( x , y , z )$ satisfy $\nabla f ( 1,0,2 ) = \vec { i } - \vec { j } + 4 \vec { k }$ .Explain why the maximum of f subject to the constraint $h ( x , y , z ) = 3$ cannot occur at the point $( 1,0,2 )$ .

---

Definitions:

Self-serving

Acting in a way that benefits oneself, often at the expense of others or ethical principles.

Conduct

The manner in which an individual behaves or performs in a professional or personal setting.

Ethical Reasoning

involves using moral principles and values to evaluate and make decisions about what is right or wrong in various situations.

Happiness

A state of well-being characterized by emotions ranging from contentment to intense joy.