document.write( "Question 73820: What is the definition of Difference Quotient and how do you arrive at an answer when you have f(x)=x^2+3x and DO= ((f(x+h)-f(x))/h \n" ); document.write( "
Algebra.Com's Answer #52786 by Edwin McCravy(20056) $\"\"$ $\"About$
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What is the definition of Difference Quotient and \r\n" );
document.write( "how do you arrive at an answer when you have \r\n" );
document.write( "f(x) = x²+3x and \r\n" );
document.write( "DQ = ((f(x+h)-f(x))/h\r\n" );
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document.write( "The difference quotient is defined as the slope of \r\n" );
document.write( "the line through the two points (x, f(x)) and \r\n" );
document.write( "(x+h, f(x+h))\r\n" );
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document.write( "          y₂ - y₁\r\n" );
document.write( "DQ = m = ---------\r\n" );
document.write( "          x₂ - x₁\r\n" );
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document.write( "      f(x+h) - f(x) \r\n" );
document.write( "DQ = --------------- \r\n" );
document.write( "       (x+h) - x\r\n" );
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document.write( "      f(x+h) - f(x) \r\n" );
document.write( "DQ = --------------- \r\n" );
document.write( "        x + h - x\r\n" );
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document.write( "      f(x+h) - f(x) \r\n" );
document.write( "DQ = --------------- \r\n" );
document.write( "            h\r\n" );
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document.write( "To find that for the given f(x):\r\n" );
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document.write( "      f(x+h) - f(x) \r\n" );
document.write( "DQ = --------------- \r\n" );
document.write( "            h\r\n" );
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document.write( "First we calculate the red part,\r\n" );
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document.write( "f(x) = x² + 3x\r\n" );
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document.write( "Replace all the x's by (x+h)\r\n" );
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document.write( "f(x+h) = (x+h)² + 3(x+h)\r\n" );
document.write( "       = (x+h)(x+h) + 3(x+h)\r\n" );
document.write( "       = x² + 2hx + h² + 3x + 3h \r\n" );
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document.write( "Now the blue part is given as\r\n" );
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document.write( "f(x) = x² + 3x  \r\n" );
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document.write( "So in\r\n" );
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document.write( "      f(x+h) - f(x) \r\n" );
document.write( "DQ = --------------- \r\n" );
document.write( "            h\r\n" );
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document.write( "replace the red f(x+h) by (x²+2hx+h²+3x+3h) and \r\n" );
document.write( "the blue f(x) by (x²+3x)\r\n" );
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document.write( "      (x²+2hx+h²+3x+3h) - (x²+3x) \r\n" );
document.write( "DQ = ----------------------------- \r\n" );
document.write( "                 h\r\n" );
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document.write( "      (x²+2hx+h²+3x+3h) - (x²+3x) \r\n" );
document.write( "DQ = ----------------------------- \r\n" );
document.write( "                 h\r\n" );
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document.write( "      x² + 2hx + h² + 3x + 3h - x² - 3x \r\n" );
document.write( "DQ = ----------------------------------- \r\n" );
document.write( "                  h\r\n" );
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document.write( "Combine like terms:\r\n" );
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document.write( "      2hx + h² + 3h \r\n" );
document.write( "DQ = --------------- \r\n" );
document.write( "            h\r\n" );
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document.write( "Factor h out of the top:\r\n" );
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document.write( "      h(2x + h + 3) \r\n" );
document.write( "DQ = --------------- \r\n" );
document.write( "            h\r\n" );
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document.write( "Cancel the h's\r\n" );
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document.write( "      1\r\n" );
document.write( "      h(2x + h + 3) \r\n" );
document.write( "DQ = --------------- \r\n" );
document.write( "            h\r\n" );
document.write( "            1\r\n" );
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document.write( "DQ = 2x + h + 3\r\n" );
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document.write( "Edwin
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