document.write( "Question 1059515: find the intervals on which f(x)= 2x^3 - 3x^2 is increasing.\r
\n" ); document.write( "\n" ); document.write( "find the intervals on which f(x)= 2x^3 - 3x^2 is concave down. \n" ); document.write( "

Algebra.Com's Answer #674574 by josgarithmetic(39618) $\"\"$ $\"About$

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The function actually has ONLY one inflection point, and based on the way a cubic function is shaped, you will expect that this f(x) will be concave down from the inflection point toward negative infinity.\r
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\n" ); document.write( "\n" ); document.write( "Again based on qualitative understanding of cubic polynomial function, you expect maybe two extreme values - one minimum and one maximum; the min is to the left and the max is to the right. Your function has actually TWO zeros.\r
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\n" ); document.write( "\n" ); document.write( "Use of the first derivative will help you find the max and min, which helps to find interval of increase ; both of the intervals.\r
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\n" ); document.write( "\n" ); document.write( "Use of the second derivative will give you the inflection point to help you with the exact interval where concave down.\r
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\n" ); document.write( "\n" ); document.write( "I had solved your first question earlier, but removed the whole solution because of (brief) trouble in dealing with second derivative and the concavity downward. \n" ); document.write( "

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