`f(x)={4x-x^3+ln(a^2-3a+3),0lt=x<3x-18 ,xgeq3` complete set of values of `a` such that `f(x)` as a local minima at `x=3` is `[-1,2]` `(-oo,1)uu(2,oo)` `[1,2]` (d) `(-oo,-1)uu(2,oo)`

Options

A. `[-1,2]`
B. `(-oo,1)cup(2,oo)`
C. `[1,2]`
D. `(-oo,-1)cup(2,oo)`

Answer

2

Explanation

clearly f(X) in decreasing just before x=3 and increasing after
`x=3 for x=3` to be the point of local minima `f(X)ltf(3^(-))`
or `-15le12-27+In(a^(2)-3a+3)`
or `a^(2)-3a+3gt3`
`or a in (-oo,1)cup(2,oo)`