anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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myininaya
  • myininaya
so far good do you know how to solve: \[\cos(\theta)=-1 \text{ for } \theta \]
anonymous
  • anonymous
no:(
myininaya
  • myininaya
have you ever seen the unit circle before?

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anonymous
  • anonymous
oh yes
myininaya
  • 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?
myininaya
  • myininaya
The x coordinates * (not do)
anonymous
  • anonymous
so pie?
myininaya
  • 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
anonymous
  • anonymous
so that would be 2x=3pi so x=pi/2 and x=3pi/2
myininaya
  • myininaya
sounds great to me :)
anonymous
  • anonymous
thanks again
myininaya
  • myininaya
np

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