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Math Help - Intervals where the function is Increasing

  1. #1
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    Intervals where the function is Increasing

    The problem is F(x) = x + cosx

    Find intervals where the function is Increasing

    I took the first derivative and I'm lost as to where to go. Any help?

    F'(x)= 1 - Sinx
    Last edited by mr fantastic; April 18th 2009 at 06:40 PM. Reason: Added the rest of the question form the title.
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  2. #2
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    Set the first derivative equal to zero. the values you get for x will be your critical points. Then, test those critical points on a number line by plugging a number on either side of each critical number to test. If the answer is negative, it is decreasing. If the answer is positive, it is increasing. Use that to figure out max and min if you need. hope that helped. =]
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  3. #3
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    So I get

    F'(x) = -Sinx/-1 = -1/-1
    F'(x) = Sinx = 1

    My trig skills are a bit rusty so I have no clue how to get the c.p. Any help ?
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  4. #4
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    My brother just told me the C.P. for this would be Pi/2.

    So from there what do I do? He just told me the answer and walked off which is pi/2 + 2kpi.

    How did he arrive at that answer?
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  5. #5
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    Quote Originally Posted by Afterme View Post
    The problem is F(x) = x + cosx

    Find intervals where the function is Increasing

    I took the first derivative and I'm lost as to where to go. Any help?

    F'(x)= 1 - Sinx
    Solve F'(x) > 0. In your case that means solving 1 - \sin x > 0 \Rightarrow \sin x < 1.

    So it should be very clear from a graph of \sin x what the intervals will be ....
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