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) = x^3 − 9x^2 + 1

Answer 1

Inc:(-∞,0) and (6,∞) Dec: (0,6)

Explanation:

You could also use derivatives or look at the graph:

f'(x)=3x^2-18x

3x^2-18x=0

x=0,6

These are your critical points.

To check if they are really critical points or if they are increasing or decreasing and to see if they aren't inflection points, plug the points back on the equation.