anonymous one year ago Find the x-coordinates where f '(x) = 0 for f(x) = 2x + sin(2x) in the interval [0, 2π]. so far I found f'(x)=2cos(2x)+2 cos(2x)=-1

1. myininaya

so far good do you know how to solve: $\cos(\theta)=-1 \text{ for } \theta$

2. anonymous

no:(

3. myininaya

have you ever seen the unit circle before?

4. anonymous

oh yes

5. myininaya

Do x coordinates of the pairs represents cos these are the numbers we want to look at can you find when the x-coordinates on the unit circle will be -1?

6. myininaya

The x coordinates * (not do)

7. anonymous

so pie?

8. myininaya

pi is going to be one solution there is another solution we were solving cos(2x)=-1 on [0,2pi] but I replaced 2x with theta so we had 0<=x<=2pi and x is theta/2 so 0<=theta/2<=2pi multiply 2 on both sides we have 0<=theta<=4pi so we actually want to solve cos(theta)=-1 on [0,4pi] but that isn't too terrible we know pi is one solution in that interval but pi+2pi is another we wanted to solve for x not theta but we know the relationship between x and theta is given by 2x=theta so we have $2x=\pi \text{ or also } 2x=\pi+2\pi$ simplify and solve for x

9. anonymous

so that would be 2x=3pi so x=pi/2 and x=3pi/2

10. myininaya

sounds great to me :)

11. anonymous

thanks again

12. myininaya

np