Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

ksandoval

use analytic methods to find the extreme values of f(x)= (1/x) + lnx on the interval 0.5 ≤ x ≤ 4 and where they occur

  • one year ago
  • one year ago

  • This Question is Closed
  1. ksandoval
    Best Response
    You've already chosen the best response.
    Medals 0

    and i know that the derivative is f'(x) = -1/x^2 + 1/x but i dont know where to go from there... lol

    • one year ago
  2. baldymcgee6
    Best Response
    You've already chosen the best response.
    Medals 1

    Where do extreme values occur?

    • one year ago
  3. ksandoval
    Best Response
    You've already chosen the best response.
    Medals 0

    i dont know thats what i need help finding.. lol. i just dont know how to find them.

    • one year ago
  4. baldymcgee6
    Best Response
    You've already chosen the best response.
    Medals 1

    okay, so in theory, extreme values will occur where the derivative of the function is equal to zero (i.e. a horizontal slope where there is maxima or minima), and they also occur where the derivative is undefined.

    • one year ago
  5. ksandoval
    Best Response
    You've already chosen the best response.
    Medals 0

    okay sooo i set the derivative equal to zero...

    • one year ago
  6. baldymcgee6
    Best Response
    You've already chosen the best response.
    Medals 1

    and...?

    • one year ago
  7. ksandoval
    Best Response
    You've already chosen the best response.
    Medals 0

    well i mean plugging in 1 for x would give you zero.

    • one year ago
  8. baldymcgee6
    Best Response
    You've already chosen the best response.
    Medals 1

    okay, so 1 is one of our critical points

    • one year ago
  9. ksandoval
    Best Response
    You've already chosen the best response.
    Medals 0

    now what do we do?

    • one year ago
  10. baldymcgee6
    Best Response
    You've already chosen the best response.
    Medals 1

    Where is f'(x) = -1/x^2 + 1/x undefined?

    • one year ago
  11. ksandoval
    Best Response
    You've already chosen the best response.
    Medals 0

    when x = 0?

    • one year ago
  12. baldymcgee6
    Best Response
    You've already chosen the best response.
    Medals 1

    exactly, but if you would notice in the question it gave us restrictions of 0.5 ≤ x ≤ 4, so we dont take 0 into account... So our critical point is 1

    • one year ago
  13. baldymcgee6
    Best Response
    You've already chosen the best response.
    Medals 1

    http://screencast.com/t/LJnPiplk

    • one year ago
  14. ksandoval
    Best Response
    You've already chosen the best response.
    Medals 0

    oooh ok. so for the answer it says: max value is 1/4 + ln4 at x = 4 min value is 1 at x = 1 local max at (1/2, 2 - ln2) how did they get the max value and local max?

    • one year ago
  15. baldymcgee6
    Best Response
    You've already chosen the best response.
    Medals 1

    Well for the max value, they just put the biggest number they could, 4, into the function, they chose 4 because of the restrictions 0.5 ≤ x ≤ 4... 4 is the biggest number, i.e. giving the biggest value.

    • one year ago
  16. baldymcgee6
    Best Response
    You've already chosen the best response.
    Medals 1

    there is no local max... so i'm not sure where they got that.. might want to ask your teacher.

    • one year ago
  17. ksandoval
    Best Response
    You've already chosen the best response.
    Medals 0

    oh.. ok. and how do they know that 1 is the min value? this is confusing for me ):

    • one year ago
  18. baldymcgee6
    Best Response
    You've already chosen the best response.
    Medals 1

    We already got that the minimum is at x = 1

    • one year ago
  19. ksandoval
    Best Response
    You've already chosen the best response.
    Medals 0

    yea but how do you know its the minimum? :\

    • one year ago
  20. baldymcgee6
    Best Response
    You've already chosen the best response.
    Medals 1

    We know it is the minimum because at that point, the derivative = 0, this is the lowest point on the curve.

    • one year ago
  21. ksandoval
    Best Response
    You've already chosen the best response.
    Medals 0

    thank you

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.