(Section 1.11: Limits and Derivatives in Calculus) 1.11.13 PART F: LINEARIZATION and MARGINAL CHANGE• The tangent lineto the graph of a functionfat the point a,fa()represents the best linear approximationto the function close to a. The tangent line model linearizesthe function locally around a. • The principle of “local linearity” states that, if the tangent line exists, the graph offresembles the line if we “zoom in” on the point a,. Example 4 (Marginal Profit; Revisiting Examples 2 and 3)If Pis a profit function, the derivative ±Pis referred to as a marginal profit (MP) function. It approximates the change in profitif we increase production by 1 unit(from 60 to 61 widgets, for instance). That is,
This is the end of the preview. Sign up
access the rest of the document.