Question

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)= - 1/x³

Explanation:

Step1: Analyze the graph

Observe the slope of the curve.

Step2: Determine increasing intervals

The function is increasing when the slope is positive. From the graph, it is increasing on $(-\infty,\infty)$.

Step3: Determine decreasing intervals

The function is decreasing when the slope is negative. There are no such intervals, so it is DNE.

Step4: Determine constant intervals

The function is constant when the slope is zero. There are no such intervals, so it is DNE.

Answer:

Increasing: $(-\infty,\infty)$
Decreasing: DNE
Constant: DNE