document.write( "Question 1020442: What is the minimum value of $\"f%28x%29=2x%2Babs%283x-1%29\"$ ? \n" ); document.write( "

Algebra.Com's Answer #636324 by Fombitz(32388) $\"\"$ $\"About$

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When $\"x%3E=1%2F3\"$ ,
\n" ); document.write( " $\"abs%283x-1%29=3x-1\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"f%28x%29=2x%2B3x-1=5x-1\"$
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\n" ); document.write( "When $\"x%3C1%2F3\"$ ,
\n" ); document.write( " $\"abs%283x-1%29=-%283x-1%29=1-3x\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"f%28x%29=2x%2B1-3x=1-x\"$
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\n" ); document.write( "So the critical point is $\"x=1%2F3\"$ , where the slope of the line goes from negative to positive.
\n" ); document.write( "So the function must be a minimum at that point.
\n" ); document.write( " $\"f%281%2F3%29=5%281%2F3%29-1=5%2F3-1=2%2F3\"$
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