You are here:
- Home
- Teens
- Homework/Study Tips
- Calculus
- Critical Numbers
Calculus/Critical Numbers
Advertisement
Question
Determine the critical number(s) of the function f(x)=2xlnx.
Please show all work so that I can understand how you got to the answer. Thank you for your help.
Hi Alex,
f(x) = 2x.lnx
We find the derivative using the product rule. The derivative of 2x is 2 and for lnx is 1/x. So,
f'(x) = 2x(1/x) + 2lnx = 2 + 2lnx
The critical number(s) occur when f'(x) = 0, i.e
2 + 2lnx = 0
lnx = -1
x = e^-1 = 1/e
and
f(x) = 2(1/e) . ln(1/e)
= (2/e).(-1)
= -2/e
Regards
- Add to this Answer
- Ask a Question
Questioner's Rating
| Rating(1-10) | Knowledgeability = 10 | Clarity of Response = 9 | Politeness = 10 |
| Comment | Thank you very much for getting back to me. Your explanation helped me a lot. | ||
Related Articles
- Orbital Name Abbreviations - Angular Momentum Quantum Numbers
- How to get the number of words in Richedit
- English-German Telephone Glossary - Telefon - Handy
- German-English Computer / Internet Glossary F-L
- 2007 Ford F-150 4x4 King Ranch - Test drive and alternative fuel vehicle review - 2007 F-150 4x4 King Ranch flex-fuel truck
Calculus
Answers by Expert:
Ahmed Salami
Expertise
I can provide good answers to questions dealing in almost all of mathematics especially from A`Level downwards. I believe i would be very helpful in calculus and can as well help a good deal in Physics with most emphasis directed towards mechanics.
Experience
An engineering graduate. I have been doing maths and physics all my life.
©2012 About.com, a part of The New York Times Company. All rights reserved.