Show That There Does Not Exist Any Function with Continuous

question 289

Essay

Show that there does not exist any function with continuous second partial derivatives in $\mathbb { R } ^ { 2 }$ such that $\frac { \delta f } { \delta x } = x ^ { 2 } y$ and $\frac { \partial f } { \partial y } = x$ .

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Definitions:

Structuralism

An early school of psychology that aimed to understand the structure of the mind by breaking down mental processes into their most basic components.

E. B. Titchener

A psychologist known for founding structuralism, focusing on breaking down mental processes into the most basic components.

Wilhelm Wundt

A German psychologist who is often regarded as the father of experimental psychology, he established the first psychology laboratory at the University of Leipzig in 1879.

Trained Introspection

A method in early psychology involving trained observers examining and reporting the content of their own thoughts and mental experiences.