document.write( "Question 50488: Given g(x) = 3x^2 - 2x + 1, find [g(a + h) - g(a)]/h.\r
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Algebra.Com's Answer #33572 by AnlytcPhil(1806)\"\" \"About 
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Given g(x) = 3x^2 - 2x + 1, find [g(a + h) - g(a)]/h. \r\n" );
document.write( "a. 6a + 3h + 1\r\n" );
document.write( "b. 6a + 3h - 1\r\n" );
document.write( "c. 6a + 3h + 2\r\n" );
document.write( "d. 6a + 3h -2\r\n" );
document.write( "e. none of these\r\n" );
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document.write( "First find g(a + h) by plugging in a + h for x in\r\n" );
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document.write( "    g(x) = 3x² - 2x + 1\r\n" );
document.write( "g(a + h) = 3(a + h)² - 2(a + h) + 1\r\n" );
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document.write( "g(a + h) = 3(a + h)(a + h) - 2a - 2h + 1\r\n" );
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document.write( "g(a + h) = 3(a² + 2ah + h²) - 2a - 2h + 1\r\n" );
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document.write( "g(a + h) = 3a² + 6ah + 3h² - 2a - 2h + 1 \r\n" );
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document.write( "Next find g(a) by plugging in a for x in\r\n" );
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document.write( "    g(x) = 3x² - 2x + 1\r\n" );
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document.write( "    g(a) = 3a² - 2a + 1\r\n" );
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document.write( "Nwxt plug (3a² + 6ah + 2h² - 2a - 2h + 1) for \r\n" );
document.write( "g(a + h) and (3a² - 2a + 1) for g(a) in\r\n" );
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document.write( "[g(a + h) - g(a)]/h \r\n" );
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document.write( "[g(a + h) - g(a)]/h = [(3a² + 6ah + 2h² - 2a - 2h + 1) - (3a² - 2a + 1)]/h\r\n" );
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document.write( "[g(a + h) - g(a)]/h = [3a² + 6ah + 3h² - 2a - 2h + 1 - 3a² + 2a - 1]/h\r\n" );
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document.write( "Cancel whatever will add to 0:\r\n" );
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document.write( "[g(a + h) - g(a)]/h = [6ah + 3h² - 2h]/h\r\n" );
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document.write( "[g(a + h) - g(a)]/h = 6ah/h + 3h²/h - 2h/h\r\n" );
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document.write( "Cancel h's in fractions:\r\n" );
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document.write( "[g(a + h) - g(a)]/h = 6a + 3h - 2\r\n" );
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document.write( "So the answer is (d)\r\n" );
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document.write( "Edwin
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