document.write( "Question 80891This question is from textbook CALCULUS
\n" ); document.write( ": For the general cubic polynomial f(x)= ax^3 + bx^2 + cx + d (a different from 0).
\n" ); document.write( "Find conditions on a, b, c, and d to ensure that f is always increasing or always decreasing on (-00, +00). \n" ); document.write( "
Algebra.Com's Answer #58030 by stanbon(75887)\"\" \"About 
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For the general cubic polynomial f(x)= ax^3 + bx^2 + cx + d (a different from 0).
\n" ); document.write( "Find conditions on a, b, c, and d to ensure that f is always increasing or always decreasing on (-00, +00).
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\n" ); document.write( "To assure Increasing:
\n" ); document.write( "The slope would have to be postive for all values of x.
\n" ); document.write( "Take the derivative: 3ax^2+2bx+c>0
\n" ); document.write( "As long as c>0 and a>0 you would get a graph (parabola) that
\n" ); document.write( "is always above the x axis. That should meet the asked-for
\n" ); document.write( "condition.
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\n" ); document.write( "To assure decreasing:
\n" ); document.write( "The slope would have to be negative for all values of x.
\n" ); document.write( "Use the same drivative but make it <0
\n" ); document.write( "Let c<0 and a<0 then you would get a graph (parabola) that
\n" ); document.write( "is always below the x-axis. That should meet the asked-for
\n" ); document.write( "condition.
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "
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