For each of the following functions, evaluate this expression. <math xmlns="http://www.w3.org/1998/Math/MathML"> <mfrac> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>+</mo> <mi>h</mi> <mo stretchy="false">)</mo> <mo>&#x2212;<!-- − --></mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mi>h</mi> </mfrac> </math>

Baladdaa9 2022-07-31 Answered
For each of the following function, evaluate this expression
f ( x + h ) f ( x ) h
1. f ( x ) = x 2 4 x + 5
2. g ( x ) = x 3 2 x + 3
3. h ( x ) = 1 2 x
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Answers (1)

akademiks1989rz
Answered 2022-08-01 Author has 16 answers
Step 1
1) f ( x + h ) f ( x ) h = ( x + h ) 2 4 ( x + h ) + 5 ( x 2 4 x + 5 ) h
= x 2 + 2 x h + h 2 4 x 4 h + 5 x 2 + 4 x 5 h
= h ( 2 x + h 4 ) h = 2 x + h 4
Step 2
2) g ( x + h ) g ( x ) h = ( x + h ) 3 2 ( x + h ) + 3 ( x 3 2 x + 3 ) h
= x 3 + 3 x 2 h + 3 x h 2 + h 3 2 x 2 h + 3 x 3 + 2 x 3 h
= h ( 3 x 2 + 3 x h + h 2 2 ) h
= 3 x 2 + 3 x h + h 2 2
Step 3
3) h ( x + h ) h ( x ) h = 1 2 ( x + h ) 1 2 x h
= 2 x 2 ( x + h ) 4 x h ( x + h )
= 2 h 4 x h ( x + h ) = 1 2 x ( x + h )
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