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document.write( "Prove that the equation \r
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document.write( "x^7+ 3x+ 3 = 0 has a unique solution.
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document.write( "I assume that you are just Calculus.\r
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document.write( "Then the solution is simple.\r
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document.write( "Take the derivative of the left side function.\r\n" );
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document.write( "It is 
, and it is always positive (for all x).\r\n" );
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document.write( "It means that the left side function itself increases monotonically when x increases.\r\n" );
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document.write( "From the other side, the left side function is NEGATIVE when x tends to 
and POSITIVE when x tends to 
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document.write( "It implies that the root does exist and is unique.\r\n" );
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document.write( "To answer next question, simply look in your calculator (or computer software) for the plot of this polynomial.\r\n" );
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document.write( "When choose two consecutive integers in a way that the function is NEGATIVE at the smaller integer and is POSITIVE at the larger one.\r\n" );
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