Question

PLEASE HELP! @Hero @ganeshie8 @amistre64

Answer 1

I already found teh critical points, but now I don't know what to do

Answer 2

Seems you should find a couple of derivatives. Go!

Answer 3

?

Answer 4

Analytical methods to find extreme values. Sounds like derivatives to me.

Answer 5

Yes, I know. Can you help?

Answer 6

Sure. What's the 1st derivative? If you don't like sec(x), try 1/cos(x).

Answer 7

the first derivative is secx tanx

Answer 8

But anyway, I already found critical points at (0,1) and (pi/ -1)

What do I do after that?

Answer 9

EDIT: (pi, - 1)

Answer 10

uh @tkhunny ?

Answer 11

@freckles @amistre64

Answer 12

What are those critical points? Minimum? Maximum? Global? Local? None of the above?

Answer 13

It is hoped that we know up front that the secant blows up at \(\pi/2\).

Answer 14

Shall we do the 2nd derivative or are we done?

Answer 15

That's what I don't know how to find out. (min, max, global, local, etc.)

Answer 16

suppose a and b are critical points with a<b

Then if you look at c<a<d<b and c,d are both greater than a then a is a min, if they are both less than a, then a is a max. If one is greater and the other is less than, then it is neither.

Or take the 2nd derivative and look at concavity