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Sketching ln graph

  • Thread starter emma3001
  • Start date
  • #1
42
0
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 Im doing this right, especially with the ln in there. Am I on the right track? What can I now do?
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618
You'd better try the first derivative again. You'll need to use both the product rule and the chain rule.
 
  • #3
378
2
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)
 
  • #4
tiny-tim
Science Advisor
Homework Helper
25,832
249
y=x(lnx)^3

6/x(lnx).
Hi emma3001! :smile:

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

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

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