find the coordinates of all points on the graph of f(x) = x + 2cos(x) in the interval [0, pie] at which the tangent line is horizontal.

Answer 1

f'(x) = 1 - 2sinx
= 0 for a horizontal slope
1-2sinx = 0
sinx = 1/2
x = π/6 or 5π/5

if x = π/6
y = π/6 + √3 = (π + 6√3)/6 ---> point (π/6 , (π+6√3)/6

if x = 5π/6
y = 5π/6 - √3 = (5π - 6√3)/6 ---> point (5π/6 , (5π-6√3)/6 )

Answer 2

thank you reiny