OpenStudy (anonymous):

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

5 years ago
OpenStudy (anonymous):

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.

5 years ago
OpenStudy (anonymous):

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

5 years ago
OpenStudy (across):

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

5 years ago
OpenStudy (anonymous):

it is a closed interval so yes..

5 years ago
OpenStudy (anonymous):

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

5 years ago
OpenStudy (across):

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

5 years ago
OpenStudy (anonymous):

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

5 years ago
OpenStudy (anonymous):

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

5 years ago
OpenStudy (across):

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

5 years ago
OpenStudy (anonymous):

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...

5 years ago
OpenStudy (anonymous):

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

5 years ago
OpenStudy (across):

I see. Thanks for clarifying. :)

5 years ago
OpenStudy (anonymous):

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

5 years ago
OpenStudy (anonymous):

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

5 years ago
OpenStudy (anonymous):

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

5 years ago
OpenStudy (anonymous):

thnx.

5 years ago