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Understanding Partial Differentiation in Functions for Horizontal Plane Analysis

Learn how to define a function in terms of two variables and analyze its vertical changes in the a-b plane by utilizing partial differentiation. Explore slopes along individual variables to evaluate changes accurately.

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Understanding Partial Differentiation in Functions for Horizontal Plane Analysis

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  1. Notation: Partial differentiation A) Explicitlydescribe function f by writing down an association rule in terms of a and b How much does fverticallychange when we jigglein the horizontala-b plane along various directions? a b

  2. Notation: Partial differentiation A) Explicitlydescribe function f by writing down an association rule in terms of a and b How much does fverticallychange when we jigglein the horizontala-b plane along various directions? B) Reserve ∂, read as “partial,” to denote slopes along one variable holding all others fixed (i.e. move only aorb, not both). Look at slope in this a b By exclusively varying this variable

  3. Notation: Partial differentiation A) Explicitlydescribe function f by writing down an association rule in terms of a and b How much does fverticallychange when we jigglein the horizontala-b plane along various directions? B) Reserve ∂, read as “partial,” to denote slopes along one variable holding all others fixed (i.e. move only aorb, not both). a b b0

  4. Notation: Partial differentiation A) Explicitlydescribe function f by writing down an association rule in terms of a and b How much does fverticallychange when we jigglein the horizontala-b plane along various directions? B) Reserve ∂, read as “partial,” to denote slopes along one variable holding all others fixed (i.e. move only aorb, not both). a b

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