How do you determine at which the graph of the function #y=x+sinx# has a horizontal tangent line?

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Answer 1 · 2017-12-29T19:37:44

Compute the first derivative
Find the value(s) of x where the first derivative is equal to 0.

Compute the first derivative:

#y' = 1 + cos(x)#

Find the value(s) of x where the first derivative is equal to 0:

#0 = 1 + cos(x)#

#cos(x) = -1#

#x = cos^-1(-1)#

The primary value is:

#x = pi#

Add integer multiples of #2pi# to obtain all of the values:

#x = pi+2npi; n in ZZ#