The maximum number of turning points in a cubic function is 2.
In this case,
[tex]f(x)=3x^3-x^2+4x-2\implies f'(x)=9x^2-2x+4[/tex]
The discriminant is [tex](-2)^2-4(9)(4)=-140<0[/tex], which means the derivative has no real roots. This means there are no critical points and thus no turning points/relative extrema.
