Answer
The graph has no horizontal tangents.
Work Step by Step
To find the slope of the tangents, we find the derivative first:
$y'=(x^3+x)'=(x^3)'+(x)'=3x^2+1$
Horizontal means a slope of $0$ which indicates that the derivative should equal $0$:
$y'=0\rightarrow3x^2+1=0\rightarrow x^2=-\frac{1}{3}$
Since over the domain of real numbers,$x^2$ cannot be negative then the above equation has no solution hence the derivative is never equal to $0$ and therefore there are no horizontal tangents.
