Fxy in a contour graph, positive or negative?

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SUMMARY

The discussion focuses on determining the mixed partial derivative fxy, which represents the rate of change of the rate of change of the function f in the x-direction with respect to y. It is established that fx is negative, indicating that as the function f decreases in the x-direction, the mixed derivative fxy needs to be evaluated to understand its behavior in the y-direction. The lack of labeled axes in the contour graph complicates the interpretation of the function's behavior.

PREREQUISITES
  • Understanding of partial derivatives, specifically mixed partial derivatives.
  • Familiarity with contour graphs and their interpretation in multivariable calculus.
  • Knowledge of the implications of negative derivatives in the context of function behavior.
  • Basic graphing skills to analyze level curves of functions.
NEXT STEPS
  • Study the properties of mixed partial derivatives in multivariable calculus.
  • Learn how to interpret contour plots and level curves for functions of two variables.
  • Explore the implications of negative partial derivatives on function behavior.
  • Review examples of calculating fxy for various functions to solidify understanding.
USEFUL FOR

Students studying multivariable calculus, educators teaching calculus concepts, and anyone interested in understanding the behavior of functions represented in contour graphs.

kougou
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Homework Statement


d=1352846320
xx.png



The question asks for fxy.
The rate of change of (the rate of change of f in the x direction) in the y-direction.


We know fx is negative because as f moves in the x-direction, f decreases. But how do I know the rate of change of fx in the y-direction? Any idea?

Thank
 
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kougou said:

Homework Statement


d=1352846320View attachment 52924The question asks for fxy.
The rate of change of (the rate of change of f in the x direction) in the y-direction. We know fx is negative because as f moves in the x-direction, f decreases. But how do I know the rate of change of fx in the y-direction? Any idea?

Thank
What is being shown in the graph? Are these level curves for z = f(x, y)?

We know fx is negative because as f moves in the x-direction, f decreases.
f is not moving. A point (x, y) in the plane is moving, which results in different values of something. I can't tell what "something" is, because your graph has no labels that would help me understand what it is conveying.
 

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