In an Exam, a Student Wrote the Following Answer $f ( x , y )$

question 82

Essay

In an exam, a student wrote the following answer.
"The level curve of $f ( x , y )$ at the point (3,-4)is $x ^ { 2 } - 2 x y = 34$ ."
How can you tell that the answer is wrong without even knowing the formula for f?

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Definitions:

Alzheimer Disease

A progressive neurodegenerative disease characterized by memory loss, cognitive decline, and eventual loss of independent function, associated with plaque accumulation and tangles in the brain.

Memory Loss

The inability to remember information or experiences, which can be temporary or permanent.

Synapses

Tiny spaces between neurons; the gaps between neurons are referred to as synaptic gaps.

Neurons

Basic working units of the nervous system, cells specialized in carrying messages through an electrochemical process.