Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
suju101
Group Title
how do i solve f(x)=secx at [pi/3,pi/6] to get global extreme values??
 2 years ago
 2 years ago
suju101 Group Title
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

shankvee\ Group TitleBest ResponseYou've already chosen the best response.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

shankvee\ Group TitleBest ResponseYou've already chosen the best response.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

across Group TitleBest ResponseYou've already chosen the best response.0
What you're stating is contradictory: You're asking to find the global values of a function... within an interval?
 2 years ago

suju101 Group TitleBest ResponseYou've already chosen the best response.0
it is a closed interval so yes..
 2 years ago

shankvee\ Group TitleBest ResponseYou've already chosen the best response.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

across Group TitleBest ResponseYou've already chosen the best response.0
Perhaps I'm misunderstanding the meaning of "global" here.
 2 years ago

shankvee\ Group TitleBest ResponseYou've already chosen the best response.1
err yeah global in this case is the given domain....
 2 years ago

shankvee\ Group TitleBest ResponseYou've already chosen the best response.1
Anyways suju this question is easier by graph method... Do you know graph of sec x?
 2 years ago

across Group TitleBest ResponseYou've already chosen the best response.0
Sorry, I'm a nitpick when it comes to word usage. :P Wouldn't those be local extrema instead?
 2 years ago

shankvee\ Group TitleBest ResponseYou've already chosen the best response.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

shankvee\ Group TitleBest ResponseYou've already chosen the best response.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

across Group TitleBest ResponseYou've already chosen the best response.0
I see. Thanks for clarifying. :)
 2 years ago

suju101 Group TitleBest ResponseYou've already chosen the best response.0
@shankee i don't know abt the graph and i am supposed to solve this theoritically.
 2 years ago

shankvee\ Group TitleBest ResponseYou've already chosen the best response.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

shankvee\ Group TitleBest ResponseYou've already chosen the best response.1
dw:1325938871185:dw Just to make it clear initially it is decreasing then increasing.
 2 years ago
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
 Engagement 19 Mad Hatter
 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.