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College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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Derivative using DELTA METHOD.

y = 4-X
Transcribed Image Text:y = 4-X
1. Increment x by small amount Ax and y by Ay. y+ Ay = f( x+ Ax) 2. Substitute y = f(x) and solve for Ay. Ay = f( x+ Ax) - f(x) 3. Perform some suitable operation to the right hand member of the result of Step 2, so that Ax will be its factor. This should be done to satisfy the limit of the quotient, that is, the limit of the denominator is not zero. 4. Divide both side of the equation by Ax. Ay_ f( x + Ax) – [(x) Ax Ax 5. Determine the limit of both sides as Ax approaches zero. lim X0 Ax = lim f( x+ Ax) – f(x) Ax Ax-0 The steps above can be summarized as follows: y = f(x) y + Ay = f( x+ Ax) Step 1 Ay = f( x+ Ax) - f(x) Steps 2 and 3 Ay f( x+ Ax) – f(x) Step 4 Ax Ax dy f( x+ Ax) - f(x) lim Ay = lim Ax-0 Step 5 dx x-0 Ax Ar ala II
Transcribed Image Text:1. Increment x by small amount Ax and y by Ay. y+ Ay = f( x+ Ax) 2. Substitute y = f(x) and solve for Ay. Ay = f( x+ Ax) - f(x) 3. Perform some suitable operation to the right hand member of the result of Step 2, so that Ax will be its factor. This should be done to satisfy the limit of the quotient, that is, the limit of the denominator is not zero. 4. Divide both side of the equation by Ax. Ay_ f( x + Ax) – [(x) Ax Ax 5. Determine the limit of both sides as Ax approaches zero. lim X0 Ax = lim f( x+ Ax) – f(x) Ax Ax-0 The steps above can be summarized as follows: y = f(x) y + Ay = f( x+ Ax) Step 1 Ay = f( x+ Ax) - f(x) Steps 2 and 3 Ay f( x+ Ax) – f(x) Step 4 Ax Ax dy f( x+ Ax) - f(x) lim Ay = lim Ax-0 Step 5 dx x-0 Ax Ar ala II
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