document.write( "Question 1067370: If f(x)=sinx+cos2x,determine which sub-intervals of (0,2pi)
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Algebra.Com's Answer #682580 by Edwin McCravy(20060)\"\" \"About 
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document.write( "If f(x)=sinx+cos2x,determine which sub-intervals of (0,2pi)\r\n" );
document.write( "f(x) is increasing on and which intervals f(x) is decreasing.\r\n" );
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document.write( "f(x) = sin(x) + cos(2x)\r\n" );
document.write( "f'(x) = cos(x) - 2sin(2x)\r\n" );
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document.write( "We set f'(x)=0 to see if there are any critical\r\n" );
document.write( "values as far as increasing or decreasing:\r\n" );
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document.write( "cos(x) - 2sin(2x) = 0\r\n" );
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document.write( "cos(x) -2[2sin(x)cos(x)] = 0\r\n" );
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document.write( "cos(x) -4sin(x)cos(x) = 0\r\n" );
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document.write( "cos(x)[1 - 4sin(x)] = 0\r\n" );
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document.write( "cos(x) = 0;   1 - 4sin(x) = 0\r\n" );
document.write( "x = \"matrix%281%2C3%2Cpi%2F2%2C%22%2C%22%2C3pi%2F2%29\"; -4sin(x) = -1\r\n" );
document.write( "                                        sin(x) = 1/4\r\n" );
document.write( "                                             x = .2527, 2.8889\r\n" );
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document.write( "Substituting test values on each interval, we find:\r\n" );
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document.write( "It's increasing on \"%28matrix%281%2C3%2C0%2C%22%2C%22%2C0.2527%29%29\"\r\n" );
document.write( "It's decreasing on \"%28matrix%281%2C3%2C0.2527%2C%22%2C%22%2Cpi%2F2%29%29\"\r\n" );
document.write( "It's increasing on  \"%28matrix%281%2C3%2Cpi%2F2%2C%22%2C%22%2C2.8889%29%29\"\r\n" );
document.write( "It's decreasing on \"%28matrix%281%2C3%2C2.8889%2C%22%2C%22%2C3pi%2F2%29%29\"\r\n" );
document.write( "It's increasing on \"%28matrix%281%2C3%2C3pi%2F2%2C%22%2C%22%2C2pi%29%29\"\r\n" );
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document.write( "The 1st green circle on the graph is where x = 0.2527\r\n" );
document.write( "The 2nd green circle on the graph is where x = \"pi%2F2\"\r\n" );
document.write( "The 3rd green circle on the graph is where x = 2.8889\r\n" );
document.write( "The 4th green circle on the graph is where x = \"3pi%2F2\"\r\n" );
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document.write( "Edwin
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