Math Notes Part 2-2

Math Notes Part 2-2 - Math Notes Part 2 Linearization o...

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Math Notes Part 2 - Linearization o Review The tangent to y = f ( x ) at x = a is y = f (a) + f 1 ( a )( x a ) o For values of x real close to a, the tangent line is a good approximation of y = f ( x ) That is, f ( x ) f ( a ) + f 1 ( a )( x a ) if x is close to a The linearization of f( x ) at x = a is: L( x ) = f ( a ) + f 1 ( a )( x a ) o Definitions The differential of x is any real number of dx The differential of y is dy = f 1 ( x ) dx o = f1x lim∆x 0∆y∆x So, for a very small x , f1x ∆y∆x So f 1 ( x ) x = y o Let dx = x Then we have f 1 ( x ) dx y So if ∆ x , is small dy We can approximate that the actual change is: = + - ( ) y∆y fx ∆x f x by = dy f1xdx - Implicit Differentiation (2.3) o If y is not defined explicitly in terms of x , you’ll need to use implicit differentiation - Related Rates (3.6) o To solve related rates of change Draw a picture Figure out which rate(s) of change you know and which you are trying to find Write an equation that relates the variables involved Differentiate both sides with respect to time Plug in specific values Attach the correct units - Graphing (3.1 and 3.2) o First Derivative Test for Rise and Fall If f 1 ( x ) changes from
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This note was uploaded on 04/17/2008 for the course MATH 11 taught by Professor Poe,laurie during the Winter '08 term at Santa Clara.

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Math Notes Part 2-2 - Math Notes Part 2 Linearization o...

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