Application of DerivativeMedium
Question
At what point the tangent line to the curve y = cos(x + y), (-2π ≤ x ≤ 2π) is parallel to x + 2y = 0
Options
A.(π/2, 0)
B.(-π/2 , 0)
C.(3π/2, 0)
D.(-3π/2, π/2)
Solution
y = cos(x + y) (-2π ≤ x ≤ 2π)
= -sin(x + y) 
(1 + sin(x + y) = -sin(x + y)
parallel to x + 2y = 0
2 sin (x + y) = 1 + sin (x + y)
sin (x + y) = 1
so x =
, y = 0
= -sin(x + y) (1 + sin(x + y) = -sin(x + y)parallel to x + 2y = 0
2 sin (x + y) = 1 + sin (x + y)
sin (x + y) = 1
so x =
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