document.write( "Question 1155431: Find the intervals on which f is increasing and the intervals on which it is decreasing.
\n" ); document.write( "f(x)= x^2 ln x^2+3 \n" ); document.write( "
Algebra.Com's Answer #778021 by ikleyn(52786)\"\" \"About 
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document.write( "    Plot y = (x^2)*(ln(x^2+3)\r\n" );
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document.write( "Looking into the formula, you can see that the function  f(x) = (x^2)*ln(x^2+3)  \r\n" );
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document.write( "    - first, is defined at all values of x (over all the domain of real numbers) and is even function,\r\n" );
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document.write( "    - and second, that it is MONOTONIC in the domain x >= 0.\r\n" );
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document.write( "Indeed, than larger the argument x is, than larger each of both factors  x^2  and ln(x^2+3) is.\r\n" );
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document.write( "So the function f(x) is monotonically increasing in the domain x >= 0.\r\n" );
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document.write( "Then from the fact that it is even function, you may conclude that the function is monotonically DECREASING in the domain  x < 0.\r\n" );
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