Question

Horizontal tangent of f(x)=x^3+x

Answer 1

f ' (x)=3x^2+1
x=square root of (-1/3)
therefore function does not have a horizontal tangent
is my conclusion correct?

Answer 2

right ,but add the word not real tangent

Answer 3

is there such a thing as a non-real tangent (ie complex tangent)?