Intervals where the function is Increasing

• April 15th 2009, 04:03 PM
Afterme
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
• April 15th 2009, 04:12 PM
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. =]
• April 15th 2009, 04:22 PM
Afterme
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 ? (Doh)
• April 15th 2009, 05:04 PM
Afterme
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?
• April 18th 2009, 06:43 PM
mr fantastic
Quote:

Originally Posted by Afterme
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 ....