document.write( "Question 1155972: Find the intervals on which f is increasing and the intervals on which it is decreasing.
\n" ); document.write( "f(x)=x^4/4 +x^3 +x^2 \n" ); document.write( "

Algebra.Com's Answer #778666 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E4%2F4+%2Bx%5E3+%2Bx%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( "find first derivative:\r
\n" ); document.write( "\n" ); document.write( " $\"f\"$ ′ $\"%28x%29=4x%5E3%2F4+%2B3x%5E2+%2B2x\"$
\n" ); document.write( " $\"f\"$ ′ $\"%28x%29=x%5E3+%2B3x%5E2+%2B2x\"$
\n" ); document.write( " $\"f\"$ ′ $\"%28x%29=x%28x%5E2+%2B3x%2B2%29\"$ \r
\n" ); document.write( "\n" ); document.write( "If $\"f\"$ ′ $\"%28x%29+%3E+0\"$ , then $\"f\"$ is $\"increasing\"$ on the interval:\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x%5E2+%2B3x%2B2%29%3E+0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%3E+0\"$ \r
\n" ); document.write( "\n" ); document.write( "or
\n" ); document.write( " $\"x%5E2+%2B3x%2B2%3E+0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x+%2B+1%29+%28x+%2B+2%29%3E0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%3E-1\"$ or $\"x%3E-2\"$ \r
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\n" ); document.write( " $\"f\"$ is $\"increasing\"$ on the intervals: \r
\n" ); document.write( "\n" ); document.write( "( $\"-2\"$ , $\"-1\"$ ) U ( $\"0\"$ , $\"infinity\"$ )\r
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\n" ); document.write( "\n" ); document.write( "and $\"f\"$ is decreasing on the interval:\r
\n" ); document.write( "\n" ); document.write( "( $\"-infinity\"$ , $\"-2\"$ ) U ( $\"-1\"$ , $\"0\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-5%2C+5%2C+-5%2C+5%2C+x%5E4%2F4+%2Bx%5E3+%2Bx%5E2%29+\"$
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