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

suju101

how do i solve f(x)=secx at [-pi/3,pi/6] to get global extreme values??

  • 2 years ago
  • 2 years ago

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

    There are two methods:- 1)Graph Do you know nature of sec x graph? 2) theory: f'(x)=sec x tan x you need to see in (-pi/6,pi/3) if it is 0,+ve or _ve.

    • 2 years ago
  2. shankvee\
    Best Response
    You've already chosen the best response.
    Medals 1

    Here f'(x)<0 when x<0 as sec x>0 and tan x<0 and f'(x)>0 for x>0 so function is decreasing for -ve x and increasing for +ve x hence max will be attained in the given interval at max possible x=pi/6

    • 2 years ago
  3. across
    Best Response
    You've already chosen the best response.
    Medals 0

    What you're stating is contradictory: You're asking to find the global values of a function... within an interval?

    • 2 years ago
  4. suju101
    Best Response
    You've already chosen the best response.
    Medals 0

    it is a closed interval so yes..

    • 2 years ago
  5. shankvee\
    Best Response
    You've already chosen the best response.
    Medals 1

    @across they're not contradictory You could have mutiple extemums in a given interval the question wants the maximun of those local maximums

    • 2 years ago
  6. across
    Best Response
    You've already chosen the best response.
    Medals 0

    Perhaps I'm misunderstanding the meaning of "global" here.

    • 2 years ago
  7. shankvee\
    Best Response
    You've already chosen the best response.
    Medals 1

    err yeah global in this case is the given domain....

    • 2 years ago
  8. shankvee\
    Best Response
    You've already chosen the best response.
    Medals 1

    Anyways suju this question is easier by graph method... Do you know graph of sec x?

    • 2 years ago
  9. across
    Best Response
    You've already chosen the best response.
    Medals 0

    Sorry, I'm a nitpick when it comes to word usage. :P Wouldn't those be local extrema instead?

    • 2 years ago
  10. shankvee\
    Best Response
    You've already chosen the best response.
    Medals 1

    Not really in a given interval what if there are two local maximums, The maximum of the two maximums is assumed to be global in this case...

    • 2 years ago
  11. shankvee\
    Best Response
    You've already chosen the best response.
    Medals 1

    Oh and in the theory part you also need to check the least value of x as f(x) is decreasing when x<0

    • 2 years ago
  12. across
    Best Response
    You've already chosen the best response.
    Medals 0

    I see. Thanks for clarifying. :)

    • 2 years ago
  13. suju101
    Best Response
    You've already chosen the best response.
    Medals 0

    @shankee i don't know abt the graph and i am supposed to solve this theoritically.

    • 2 years ago
  14. shankvee\
    Best Response
    You've already chosen the best response.
    Medals 1

    Err okay so f'(x)<0 at x<0 means function is initially decreasing. Then at x=F'(x)=0 as tanx=0 so tangent is horizontal and f'(x)>0at x>0 implies function increases afterwards. Now theoratically the maximum could occur at two points which are the two end points THis is bcoz All values in between them in their nieghbourhood will be less than them. So just plug in the end points whichever gives greater value is the answer

    • 2 years ago
  15. shankvee\
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1325938871185:dw| Just to make it clear initially it is decreasing then increasing.

    • 2 years ago
  16. suju101
    Best Response
    You've already chosen the best response.
    Medals 0

    thnx.

    • 2 years 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.