Question 1059515: find the intervals on which f(x)= 2x^3 - 3x^2 is increasing.
find the intervals on which f(x)= 2x^3 - 3x^2 is concave down.
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! 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.
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.
Use of the first derivative will help you find the max and min, which helps to find interval of increase ; both of the intervals.
Use of the second derivative will give you the inflection point to help you with the exact interval where concave down.
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.
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