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