Find the x-coordinates of all points on the curve at which the tangent line is horizontal. I don't know what to do and where to begin.
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Originally Posted by FalconPUNCH! Find the x-coordinates of all points on the curve at which the tangent line is horizontal. I don't know what to do and where to begin. the tangent line is horizontal when the derivative is zero. find the derivative, set it equal to zero and solve for x
Originally Posted by Jhevon the tangent line is horizontal when the derivative is zero. find the derivative, set it equal to zero and solve for x Thanks I'll try that.
I got as the derivative and I pretty much don't know how to solve it for x.
Originally Posted by FalconPUNCH! I got as the derivative and I pretty much don't know how to solve it for x. that's because your derivative is incorrect
Originally Posted by Jhevon that's because your derivative is incorrect could you please explain how you got that because every time I try I get a different answer.
Originally Posted by FalconPUNCH! could you please explain how you got that because every time I try I get a different answer. for the first part we use the chain rule: for : and the other piece is trivial. so
Originally Posted by Jhevon for the first part we use the chain rule: for : and the other piece is trivial. so Oh I know what I did wrong. I forgot to take the -2 like this
Originally Posted by FalconPUNCH! Oh I know what I did wrong. I forgot to take the -2 like this ok. now set the derivative to zero and continue
Originally Posted by Jhevon ok. now set the derivative to zero and continue I got cos2x = cosx
Originally Posted by FalconPUNCH! I got cos2x = cosx are you forgetting your identities? this is quadratic in cos(x). you can take it from here right?
Originally Posted by Jhevon ok. now set the derivative to zero and continue Originally Posted by Jhevon are you forgetting your identities? this is quadratic in cos(x). you can take it from here right? To tell you the truth I can't remember any of the identities since I haven't used them in a year. I'll try and take it from there.
Originally Posted by FalconPUNCH! To tell you the truth I can't remember any of the identities since I haven't used them in a year. I'll try and take it from there. you should look them up. for double angles you must know that: ok, continue. tell me if you have any problems
Originally Posted by Jhevon you should look them up. for double angles you must know that: ok, continue. tell me if you have any problems Yeah I don't think I can do it. I'm just going in circles. I was never good with functions
Originally Posted by FalconPUNCH! Yeah I don't think I can do it. I'm just going in circles. I was never good with functions are you taking me for a ride? or are you really trying? *suspicious smiley (we still need one of these)* ....this is a quadratic, see if you can factorize what angles does this happen for?
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