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## Homework Statement

For all ##a,b \, \in \, R##, the function ##f(x)=3x^4-4x^3+6x^2+ax+b## has:

a) no extremum

b) exactly one extremum

c) exactly two extremum

d) three extremum

## Homework Equations

## The Attempt at a Solution

##f'(x)=12x^3-12x^2+12x+a=12x(x^2-x+1)+a##

If a=0, there is one extremum but how what about the other values of a? The given answer is b and using a=0 gives the answer. What if for some other value of a there are more than one extremum.

Any help is appreciated. Thanks!