Question

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

Answer 1

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

Explanation:

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`