Finding the absolute maximum and absolute minimum

[meeklobraca]

Homework Statement

Find the absolute max and min of

f(t)=t + cot(t/2) on [pi/4, 7pi/4]

Homework Equations

The Attempt at a Solution

I have attempted to find the derivative which I believe is

1 - csc^2 (t/2) * (t/2) which I can simplify down to cot^2 (t/2) * (t/2)

Even if that is correct, which I am doubtful of, where do I go from here?

Thank You!

 

[Dick]

Why do you think the derivative of t-cot(t/2) is 1-(csc^(t/2))*(t/2)? Better fix that before you try to proceed.

 

[meeklobraca]

Okay I've found the derivative of t + cot (t/2) to be

1 - csc^2(t/2) * 1/2

 

[Dick]

Okay I've found the derivative of t + cot (t/2) to be

1 - csc^2(t/2) * 1/2

That's much better. So do you have any critical points on [pi/4, 7pi/4]?

 

[meeklobraca]

Here in lies the problem Dick. Where do you go from here?

im at sqrt 2 = csc (t/2) from which I've turned into sqrt 2 = 1/sin (t/2)

 

[Dick]

That's pretty good progress. Actually possibilities are at sin(t/2)=+/-1/sqrt(2). Can you draw a graph of sin(x) and tell me where sin(x)=+/-1/sqrt(2)? Then put t/2=x. I happen to know sin(pi/4)=1/sqrt(2).