Find the values of x on the curve y = cos(x) 2 + sin(x) at which the tangent is horizontal.

Answer 1

y = cos²x + sinx

Horizontal tangent when y' = 0

-2cosxsinx + cosx = 0

cosx(-2sinx + 1) = 0

cosx = 0 or sinx = 1/2

cosx = 0 when x = π/2 or 3π/2

sinx = 1/2 when x = π/6 or 5π/6

Solutions in the interval [0, 2π] are π/2, 3π/2, π/6, and 5π/6