document.write( "Question 1189314: A function f(x) = x3 + 2x - 1 has a zero within (0.1). Find the interval that the zero exists.
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Algebra.Com's Answer #820649 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "A function f(x) = x3 + 2x - 1 has a zero within (0.1). Find the interval that the zero exists.
\n" ); document.write( "(A) (0.1, 0.3) (B) (0.4, 0.5) (C) (0.6, 0.7) (D) (0.7. 0.9)
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document.write( "Notice that the given function is monotonic.  It is clearly seen by an unarmed eye, \r\n" );
document.write( "since it is the sum of two monotonic functions;\r\n" );
document.write( "but also can be proved if you will take the derivative.\r\n" );
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document.write( "Since the function is monotonic, it has a UNIQUE zero inside interval (0,1).\r\n" );
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document.write( "It means, that in any given interval this function has the zero inside this interval if and only if \r\n" );
document.write( "the values of the function at endpoints of the interval have opposite signs.\r\n" );
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document.write( "Having this said, the rest is a straightforward checking.\r\n" );
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document.write( "The answer is option (B).\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is the way to determine the interval, containing the root, by computing the values of the given function ONLY,\r
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