Absolute Extrema: f(x) = csc(x)

[2000WS6]

Having a problem (mostly because of the presence of trig functions). I understand the mechanics (I think) but I'm afraid I've gone wrong in my work somehwere. This is 1st semester calculus. Here's my work...

Let f*(x) = the derivative of f(x)

f(x) = csc x [(pi/6), (3pi/4)]

f*(x) = -(csc x)(cot x)

-> -(csc x)(cot x) = 0

- csc x = 0 cot x = 0
*undefined x = (pi/2) **critical number

Evaluate at critical number...
f (pi/2) = 1

Evaluate at endpoints...
f (pi/6) = 2

f (3pi/4) = (sq root of) 2

Maximum ((pi/6), 2)
Minimum ((3pi/4), (sq root) 2)


That's what I've got to the best of my knowledge but I question it. Sorry if my notation is messy - this is my first time on a math forum and my first time asking for help. I did skim the rules and tried to post in accordance with them so don't grill me, just let me know if there's something I need to change for the next time I ask for help.

Thanks for any help.

 

[stapel]

What is the actual exercise? What are its instructions?

Please be complete. Thank you!

Eliz.

 

[Dr. Flim-Flam]

All is Ok except you min is f(Pi/2) = 1

 

[2000WS6]

Re:

What is the actual exercise? What are its instructions?

Please be complete. Thank you!

Eliz.

Directions are to find all absolute extrema on the closed interval (stated in the original problem).

To Dr. Flim-Flam, are you saying that my critical point is also my minimum, not the one I currently have there? I'm confused. Thank you for the help!

 

[Dr. Flim-Flam]

1 < sqrt(2)

 

[2000WS6]

1 < sqrt(2)

Sorry - had a brain fart. Thanks!