Partial differentiation Flashcards
Dependent variable is …
a variable whose value is determined by that taken by the independent variables;
in z=f(x,y), the dependent variable is z.
Independent variables are …
variables whose values determine that of the dependent variable;
in z=f(x,y), the independent variables are x and y.
Function of two variables …
a rule that assigns to each pair of incoming numbers, x and y, a uniquely defined outgoing number, z.
Differentials are …
limiting values of incremental changes.
Implicit differentiation is …
the process of obtaining dy/dx where the function is not given explicitly as an expression for y in terms of x.
When we deal with functions of 2 variables y=f(x,y) then we obtain two first-order partial derivatives ∂f/∂x and ∂f/∂y by …
differentiating with respect to one variable at a time, keeping the remaining variable fixed.
We apply small increment formula when …
we need to evaluate the net change in a function z=f(x,y), if x and y change simultaneously.
Objective function is …
a function that one seeks to optimize (usually) subject to constraints.
Lagrange multiplier is applied for …
solving constrained optimization problems, especially when we handle non-linear constraints and problems involving more than two variables.
Lagrange multiplier is …
the number λ which is used in the Lagrangian function. In economics this gives the change in the value of the objective function when the value of the constraint is increased by 1 unit.
