Find the number of points of local extrema of `f(x)=3x^4-4x^3+6x^2+ax+b` where `a,b in R`

Explanation

We have
`f(x) = 3x^(4) - 4x^(3) + 6x^(2) + ax + b`
`therefore (dy)/(dx) = 12x(x^(2) - x + 1) + a`
`rArr (d^(2)y)/(dx^(2)) = 12(3x^(2) - 2x + 1) gt 0`
So, `(dy)/(dx)` is an increasing function.
But `(dy)/(dx)` is polynomial of degree 3.
So, it has exactly one real root. Thus, derivative becomes zero at exactly one point.