How do you find the points on the curve #y=x+2cosx# that have a horizontal tangent line?

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Answer 1 · 2017-11-02T16:12:58

See below.

We know that horizontal tangents occur where the derivative equals #0#. So we first need to differentiate the function.

#dy/dx (x+2cos(x)= 1-2sin(x)#

We need to find values of #x# that give #1-2sin(x)=0#

#:.#

#sin(x)= 1/2=> x= -(7pi)/6 , - (11pi)/6 , pi/6 , (5pi)/6#

For:

#-2pi<= x <= 2pi#

Graph of #y = x+cos(x)#

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