Sketching y = x(ln x)³

[emma3001]

I have to sketch the following function:
y=x(lnx)^3

The ln scares me a bit... I have found the derivative of the function as 3(lnx)^2, and when making that equal to zero I got an anwer of around 0.7 if i remember correctly. This I guess is my critical number? Then the second derivative is 6/x(lnx). I really am not sure if I am doing this right, especially with the ln in there. Am I on the right track? What can I now do?

 

[Dick]

You'd better try the first derivative again. You'll need to use both the product rule and the chain rule.

 

[rootX]

You are missing one term:
it should be
[..]+6*log(x)/x

yep, so you are maximum points are wrong..
you should be getting
1.0000
0.0498

ignore what the thing is.. find values when function is max, and see if f^2 is positive for x>0 ...

I would use software like "Graph: padowan.dk
and my calculator (plugging in different values)

 

[tiny-tim]

y=x(lnx)^3

6/x(lnx).

Hi emma3001!

Hint: try it for cosx instead of lnx, and then adapt.

So try y=x(cos)^3, and y = 6/x(cosx).