Question

Find all points on the graph of the function f(x) = 2 cos(x) + (cos(x))2 at which the tangent line is horizontal. Consider the domain x = [0,2π).

[ , ] (Smaller x values)

Answer 1

A horizontal line has slope zero, the slope of the tangent line is given by deriving the function.

f(x)' = 0
f(x)' = 2 * ( - sin (x) ) + 2 cos (x) (-sin (x)) = 0
f(x)' = - 2 sin x - 2 sin x cos x = 0
x = 0 or pi or 2 pi