Hello, I am suck on this question and when through 1 tutor in person and 2 online tutors with no success (they could not get the solution, no joke) can someone help me out. The question is...

 

Find the interval(s) in [ 0 , 2 ] on which the following function is increasing and those on which it is decreasing.

 

f(t) = - sin t - cos t

 

 

Any help would be great thanks!

 

Tacobell

Two easy ways:

 

You can draw it.

 

Or you can take the derivative and set it to 0 to find all the turning points(which will break it into sub regions) and test each region to see if it is positive or negative.

I got the derivative and set it equal to zero and that is where the problems started, what are the critical numbers you got, if you don't mind.

 

 

Tacobell

In the interval [0,2], I get a single turning point of [math]\pi/4[/math]. If you didn't get this, you should put your working up and see where you went wrong.

I got that. I then made a sign chart, [-----------pi/4-----------] and tested the CN's to see that on the left the derivative output is a negative number (this means that on this segment the function is decreasing) and to the left a positive number (meaning that the function is ascending).

 

Ascending: [pi/4, 2pi]

Descending: [0, pi/4]

 

this is incorrect, I don't see where I am going wrong.

 

Tacobell

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Merged post follows:

Consecutive posts merged

I found the answer if anyone is wondering,

 

Increasing: (pi/4, 5pi/4)

 

Decreasing: (0, pi/4) U (5pi/4, 2pi)

Then your original answer was correct. It didn't ask for the the regions outside the given range.

Tacobell, in the first post, is your range supposed to be [math][0,2\pi][/math] instead of [math][0,2][/math]?

oops, it is [0, 2pi]