Find the points where the tangent line is parallel to x-axis. x^3 + 3x +14
The slope of the tangent line to the curve parallel to the x-axis will be the point(s) where the first derivative is zero:
There is no real solution for this, thus there is no tangent line to the given function parallel to the x-axis.
Note that the function is increasing for all real x, so the first derivative is positive everywhere.