document.write( "Question 1007809: The maximum value of f(x) = x3 – 3x2 – 9x + 2 on the interval [0, 6] is\r
\n" ); document.write( "\n" ); document.write( " 2
\n" ); document.write( " 56
\n" ); document.write( " 135
\n" ); document.write( " There is no maximum on [0, 6] \n" ); document.write( "

Algebra.Com's Answer #623673 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "The maximum value of f(x) = x3 – 3x2 – 9x + 2 on the interval [0, 6] is
\n" ); document.write( "2
\n" ); document.write( "56
\n" ); document.write( "135
\n" ); document.write( "There is no maximum on [0, 6]
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document.write( "Take the derivative of f(x). It is\r\n" );
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document.write( "f'(x) = .\r\n" );
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document.write( "Equal it to zero and find the roots:\r\n" );
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document.write( " = ,\r\n" );
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document.write( " = ,\r\n" );
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document.write( "(x+1)*(x-3) = 0.\r\n" );
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document.write( "The roots are x = -1, x = 3.\r\n" );
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document.write( "They are the candidates for maximum/minimum of f(x).\r\n" );
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document.write( "To check further, look into the second derivative of f(x) at these values of x.\r\n" );
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document.write( "f''(x) = 6x - 6;\r\n" );
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document.write( "f''(-1) = 6*(-1) -6 = -12; f''(3) = 6*3-6 = 12.\r\n" );
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document.write( "Hence, x = -1 is the maximum, and x = 3 is the minimum.\r\n" );
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document.write( "The plot of f(x) below confirms this analysis.\r\n" );
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document.write( "Plot of f(x) =  –  –  + \r\n" );
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