document.write( "Question 1202783: (f(x+h)-f(x))/(h) Let f(x) = -2x^(2)- x + 3
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Algebra.Com's Answer #837880 by math_tutor2020(3817) $\"\"$ $\"About$

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\n" ); document.write( "Answer: -4x-2h-1\r
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\n" ); document.write( "\n" ); document.write( "Work Shown:\r
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\n" ); document.write( "\n" ); document.write( "We first compute f(x+h)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29+=+-2x%5E2-x%2B3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%2Bh%29+=+-2%28x%2Bh%29%5E2-%28x%2Bh%29%2B3\"$ Each x replaced with (x+h).\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%2Bh%29+=+-2%28x%2Bh%29%28x%2Bh%29-x-h%2B3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%2Bh%29+=+-2%28x%5E2%2B2xh%2Bh%5E2%29-x-h%2B3\"$ FOIL rule\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%2Bh%29+=+-2x%5E2-4xh-2h%5E2-x-h%2B3\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now subtract off f(x)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%2Bh%29-f%28x%29+=+%28-2x%5E2-4xh-2h%5E2-x-h%2B3%29+-+%28-2x%5E2-x%2B3%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%2Bh%29-f%28x%29+=+-2x%5E2-4xh-2h%5E2-x-h%2B3+%2B+2x%5E2%2Bx-3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%2Bh%29-f%28x%29+=+-4xh-2h%5E2-h\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%2Bh%29-f%28x%29+=+h%28-4x-2h-1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "The last step is to divide over h.\r
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\n" ); document.write( "\n" ); document.write( " $\"%28f%28x%2Bh%29-f%28x%29%29%2Fh+=+%28h%28-4x-2h-1%29%29%2Fh\"$ \r
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\r
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\n" ); document.write( "\n" ); document.write( " $\"%28f%28x%2Bh%29-f%28x%29%29%2Fh+=+%28cross%28h%29%28-4x-2h-1%29%29%2F%28cross%28h%29%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"%28f%28x%2Bh%29-f%28x%29%29%2Fh+=+-4x-2h-1\"$ \r
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\n" ); document.write( "\n" ); document.write( "Note: As h approaches 0, then $\"-4x-2h-1\"$ approaches $\"-4x-1\"$ which is the derivative of $\"f%28x%29+=+-2x%5E2-x%2B3\"$ .
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