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

Answer 1

The tangent is horizontal where the derivative y' is 0.

y' = -sin(x)/2 + cos(x)

Set that to 0 and solve for x:

-sin(x)/2 + cos(x) = 0

2cos(x) = sin(x)

tax(x) = 2

x = 1.1 + kπ (for any integer k)