The slope of the tangent line to [tex]f(x)[/tex] through the point [tex](x,f(x))[/tex] is given by the derivative:
[tex]f(x)=e^{-\cos x}\implies f'(x)=e^{-\cos x}\sin x[/tex]
The value of the derivative is zero when [tex]\sin x=0[/tex], which happens for infinitely many points [tex]x=n\pi[/tex] where [tex]n[/tex] is any integer.
