Question

Determine the interval(s) on which the function is increasing and decreasing. (enter your answers using interval notation. if an answer does not exist, enter dne.)

Answer 1

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