Find intervals of increase and decrease of f(x) = (x^3)(2x^2)

[KJL]

I'm stuck! the question is: Find the intervals of increase and decrease of f(x) = (x^3)(2x^2)

 

[stapel]

I'm stuck! the question is: Find the intervals of increase and decrease of f(x) = (x^3)(2x^2)

This function simplifies as "f(x) = 2x⁵". It's a simple polynomial function with exactly one zero. From the first derivative, you know where the one critical point is, and you know (from what you learned back in algebra about even-powered polynomials, etc) that the derivative function is always elsewhere positive.

So where are you stuck? Please be complete, showing all of your steps and reasoning so far. Thank you!