f(x)=(x−1)(x−2)(x−3) has a local minima when x is equal to
A
3+1√2
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B
3−1√2
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C
2+1√3
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D
2−1√3
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Solution
The correct option is C2+1√3 f(x)=(x−1)(x−2)(x−3) ⇒f(x)=x3−6x2+11x−6
Differentiate w.r.t. x f′(x)=3x2−12x+11
From f′(x)=0⇒x=12±√144−1326 ⇒x=2±1√3
Let f′(x)=(x−α)(x−β),α<β
and α=2−1√3,β=2+1√3
Since, sign of f′(x) changes from negative to positive as x crosses β from left to right, therefore x=β is a point of local minima.