document.write( "Question 87220: Determine, approximately using a graph, the intervals on which the function
\n" ); document.write( "f(x)=x^3 + 3x^2-7x-1 is increasing and decreasing. \n" ); document.write( "
Algebra.Com's Answer #63164 by Nate(3500)\"\" \"About 
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f(x) = x^3 + 3x^2 - 7x - 1
\n" ); document.write( "A function will change from decreasing to increasing or vise versa after hitting a peak or a valley (a minima or maxima).
\n" ); document.write( "\"graph%28300%2C300%2C-5%2C5%2C-5%2C20%2Cx%5E3+%2B+3x%5E2+-+7x+-+1%29\"
\n" ); document.write( "Approx. at -3 and 1 the function changes signs.
\n" ); document.write( "Exact:
\n" ); document.write( "f(x) = x^3 + 3x^2 - 7x - 1
\n" ); document.write( "f'(x) = 3x^2 + 6x - 7
\n" ); document.write( "0 = 3x^2 + 6x - 7
\n" ); document.write( "7 = 3x^2 + 6x
\n" ); document.write( "7/3 = x^2 + 2x
\n" ); document.write( "10/3 = (x + 1)^2
\n" ); document.write( "-1 +- sqrt(10/3) = x
\n" ); document.write( "When: x < -1 - sqrt(10/3) .. the function is increasing
\n" ); document.write( "When: -1 - sqrt(10/3) < x < -1 + sqrt(10/3) .. the function is decreasing
\n" ); document.write( "When: -1 + sqrt(10/3) < x .. the function is increasing again \n" ); document.write( "
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