Show That There Does Not Exist Any Function $f ( x , y )$

question 159

Essay

Show that there does not exist any function $f ( x , y )$ with continuous second partial derivatives such that $\frac { \delta f } { \delta x } = 2 y$ and $\frac { \partial f } { \partial y } = - 2 x$

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Definitions:

Flooding

a behavioral therapy technique used to treat phobias and anxiety disorders by exposing the patient to their fear at its most extreme intensity, without any gradual build-up.

Paradoxical Intent

A therapeutic technique where individuals are encouraged to engage in or intensify their feared behaviors, often leading to a decrease in the feared symptom's intensity.

Aversion Therapy

A form of psychological treatment using negative stimuli to reduce or eliminate unwanted behaviors or attractions.

Modeling

The process of learning by observing and imitating the behavior of others.