Increasing/Decreasing Function Question

[Tacobell]

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

[ydoaPs]

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.

[Tacobell]

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

[Dave]

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.

[Tacobell]

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)

[ydoaPs]

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

[Dave]

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

[Tacobell]

oops, it is [0, 2pi]