Question

Hello, I would greatly appreciate your input.

I just need some reassurance that I'm going about this question the right way. I am to find out where h(x)=x*(x-1)^(1/3)is increasing and decreasing. so after I did some solving I found my critical points to be x=(3/4) and x=1.

I tested for some values and stated that h is decreasing at the following intervals: (-∞,3/4) and (3/4,1) and is increasing at (1,∞).

Is this correct? I'm just confused because when I check on a graphing device, it does not show the functions x intervals from (-∞,1), but I thought that this function would have x as a set of real numbers. Am I wrong? If so, please tell me the correct way to go about this.

Thank you for your time. :)

Answer 1

I don't know what you are using to graph your function, but I find this site extremely useful
http://rechneronline.de/function-graphs/

It lets you graph more than one function and it lets you change the ranges for for both x and y

I entered x*(x-1)^(1/3) with the
x-range from -1 to 2 to show your x=3/4 is correct to produce a local minimum.
Experiment with the y-range to get a closer look at the function

Answer 2

:O This graphing device is much better! I was using an application made by google chrome x). Thank you so much, I'll use this from now on :)