sols3 - SOLUTIONS TO HOMEWORK ASSIGNMENT #3 1. Each of the...

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SOLUTIONS TO HOMEWORK ASSIGNMENT #3 1. Each of the following questions can be done with little computation. Suppose f ( x ), g ( x ) are functions satisfying f ( a )= α, g ( a )= β, f 0 ( a )= γ and g 0 ( a )= δ for some a, α, β, γ, δ. (a) Compute the derivative of f ( x )+ g ( x )at x = a . (b) Compute the derivative of f ( x ) g ( x )at x = a . (c) Compute the derivative of f ( x ) /g ( x )at x = a . (d) Compute the derivative of x 2 f ( x ) - x 3 g ( x )at x = a . Solutions: (a) d dx ( f ( x )+ g ( x )) ± ± x = a =( f 0 ( x )+ g 0 ( x )) ± ± x = a = f 0 ( a )+ g 0 ( a )= γ + δ. (b) d dx ( f ( x ) g ( x )) ± ± x = a =( f 0 ( x ) g ( x )+ f ( x ) g 0 ( x )) ± ± x = a = f 0 ( a ) g ( a )+ f ( a ) g 0 ( a )= γβ + αδ (c) d dx ² f ( x ) g ( x ) ³ ± ± ± x = a = g ( x ) f 0 ( x ) - f ( x ) g 0 ( x ) ( g ( x )) 2 ± ± ± x = a = βγ - αδ β 2 (d) d dx ( x 2 f ( x ) - x 3 g ( x ) ) ± ± ± x = a = ( 2 xf ( x )+ x 2 f 0 ( x ) - 3 x 2 g ( x ) - x 3 g 0 ( x ) ) ± ± ± x = a =2 + a 2 γ - 3 a 2 β - a 3 δ 2. Each of the following questions can be done with little computation. Suppose
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This note was uploaded on 01/12/2010 for the course STAT 100 taught by Professor Denissjerve during the Winter '06 term at San Jose State University .

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sols3 - SOLUTIONS TO HOMEWORK ASSIGNMENT #3 1. Each of the...

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