Respuesta :
So, The open intervals for the are : Increasing on: (−∞,0),(2,∞),
Decreasing on: (0,2), Constant is DNE.
Here, the function is f(x) = x³ − 3x² + 2, the open interval out here is termed as the interval which is indicated by parentheses and the endpoints are not included.The increasing and decreasing terms are the response of the function related to the intervals, it determined the derivative of the function.
If f′(x)>0 for a given open interval, then the function is said to increase on the interval, whereas if f′(x)<0 for the given interval, then it is said that the function is decreasing on the given interval and if f′(x)=0, then the function is said to be constant for the interval .
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Determine the open intervals on which the function is increasing, decreasing, or constant. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)
f(x) = x³ − 3x² + 2
