erandväärtuselisel

Erandväärtuselisel is a term used in Estonian mathematics and economics to describe the surface that represents marginal values of a multivariable function. The concept centers on the idea of marginal value, or erandväärtus, which measures how much the value of a function changes when a single input variable changes by a small amount while other inputs are held constant.

Formally, for a differentiable function f: R^n -> R, the marginal value with respect to the i-th variable is the partial derivative ∂f/∂x_i. The erandväärtuselisel, or marginal value surface, is the set of points in the augmented space (x_1, ..., x_n, m) such that m = ∂f/∂x_i(x_1, ..., x_n). In a two-variable example, this yields a three-dimensional surface in (x, y, m) space that shows how the marginal value with respect to x_i varies with the inputs.

In practical terms, the marginal value surface provides a geometric visualization of how sensitive the function is to small changes in a given input. This is useful in optimization, sensitivity analysis, and economic interpretations of marginal productivity or marginal utility. It complements the gradient by focusing on the single-variable dependence rather than the full vector of changes.

While the exact terminology can vary by text, the underlying idea remains: the erandväärtuselisel is the surface that maps input configurations to their corresponding marginal values for a chosen variable, illustrating how incremental changes propagate through the system. See also marginal value, partial derivative, gradient, and level sets.

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