## sandy524 Group Title find the derivative of f(x) = cos(x) − sin^2(x) on [0,2pi] one year ago one year ago

1. sandy524 Group Title

i now know that its -sin(x)(2cos(x)+1)

2. sandy524 Group Title

can yu guys help me find the critical points

3. myininaya Group Title

Are you sure it ask you to find f'(x) on [a,b]?

4. myininaya Group Title

If so, you did that. You are done.

5. sandy524 Group Title

yes. may you help me find the critical points of this now

6. myininaya Group Title

Set f'(x)=0 and solve for x to find the critical numbers.

7. myininaya Group Title

You only need to solve this on the interval [0,2 pi]

8. sandy524 Group Title

can we do it together please

9. myininaya Group Title

You are already factored f'(x) Now set both factors equal to 0.

10. sandy524 Group Title

how? can we work out the problem

11. sandy524 Group Title

12. myininaya Group Title

Yes. I'm walking you through it. You have -sin(x)*(1+2cos(x))=0 Set both factors equal to 0.

13. sandy524 Group Title

ok

14. myininaya Group Title

Just like if you have a*b=0 then either a=0 or b=0 or both=0

15. sandy524 Group Title
16. sandy524 Group Title

this is all i have

17. sandy524 Group Title

18. myininaya Group Title

Use your unit circle. Keep in mind you only have to look between 0 and 2pi

19. myininaya Group Title

You have -sin(x)=0 or 1+2cos(x)=0 Solve both of these for the trig function. Solve the first one for sin(x) and solve the second one for cos(x). Tell me what you get after doing this.

20. sandy524 Group Title

-sinx=pin

21. sandy524 Group Title

$\pi n$

22. myininaya Group Title

Well you are trying to solve -sin(x)=0 for x. You could divide both sides by -1 since -1 will never be 0. Try solving this: sin(x)=0 Then we will come back to 1+2cos(x)=0