Calculus
posted by Tim .
Find all points on the graph of the function
f(x) = 2 cos x + cos^2 x
at which the tangent line is horizontal. (Use n as your arbitrary integer.)
smaller yvalue (x,y)=
larger yvalue (x,y)=

Since the derivative is the slope of the tangent line, we need
2sinx  2cosx*sinx = 0
2sinx(1+cosx) = 0
sinx = 0 means x = nπ
cosx = 1 means x = (2n+1)π
so, f(x) has a horizontal tangent at x=nπ