Precalc0110to0111-page24 - (Section 1.11: Limits and...

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(Section 1.11: Limits and Derivatives in Calculus) 1.11.13 PART F: LINEARIZATION and MARGINAL CHANGE • The tangent line to the graph of a function f at the point a , fa () represents the best linear approximation to the function close to a . The tangent line model linearizes the function locally around a . • The principle of “ local linearity ” states that, if the tangent line exists, the graph of f resembles the line if we “zoom in” on the point a , . Example 4 (Marginal Profit; Revisiting Examples 2 and 3) If P is a profit function, the derivative ± P is referred to as a marginal profit ( MP ) function . It approximates the change in profit if we increase production by 1 unit (from 60 to 61 widgets, for instance). That is,
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This document was uploaded on 12/29/2011.

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