document.write( "Question 62424: If f(x)=x(x-1)(x-4)^2, use interval notation to give all values of x where f(x)>0. \n" ); document.write( "
Algebra.Com's Answer #43182 by funmath(2933)\"\" \"About 
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If f(x)=x(x-1)(x-4)^2, use interval notation to give all values of x where f(x)>0.
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\n" ); document.write( "Find the places where the f(x)=0, some books call them critical numbers. This will tell you what the possible intervals are.
\n" ); document.write( "x=0 and x-1=0 and x-4=0
\n" ); document.write( "x=0 and x=1 and x=4
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\n" ); document.write( "The intervals to test are: (-infinity,0), (0,1), (1,4) and (4,infinity)
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\n" ); document.write( "Pick a test number from each inveral, if it's >0 then the interval is part of the soltuion, if not, it's not.
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\n" ); document.write( "For (-infinity,0) test x=-1.
\n" ); document.write( "-1(-1-1)(-1-4)^2>0 ?
\n" ); document.write( "-1(-2)(-5)^2>0 ?
\n" ); document.write( "-1(-2)(25)>0 ? An even number of negatives is +.
\n" ); document.write( "50>0 This is true so (-infinity,0) is part of the solution.
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\n" ); document.write( "For (0,1) test x=1/2
\n" ); document.write( "1/2(1/2-1)(1/2-4)^2>0 ?
\n" ); document.write( "1/2(-1/2)(-7/2)^2>0 ?
\n" ); document.write( "1/2(-1/2)(49/4)>0 We don't have to solve this to see that it's negative because an odd number of negatives is -.
\n" ); document.write( "(0,1) is rejected.
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\n" ); document.write( "For (1,4) test x=3
\n" ); document.write( "3(3-1)(3-4)^2>0
\n" ); document.write( "3(2)(-1)^2>0
\n" ); document.write( "3(2)(1)>0 No positive means this is positive, therefore (1,4) is part of the solution.
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\n" ); document.write( "For (4,infinity) test x=5
\n" ); document.write( "5(5-1)(5-4)^2>0
\n" ); document.write( "5(4)(1)^2>0
\n" ); document.write( "5(4)(1)>0 No positive means this is positive, therefore (4,infinity) is part of the solution set.
\n" ); document.write( "Therefore the solution set is: (-infinity,0)U(1,4)U(4,infinity)
\n" ); document.write( "Happy Calculating!!! \n" ); document.write( "
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