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Question

f(x)=(x1)(x2)(x3) has a local minima when x is equal to

A
2+13
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B
213
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C
312
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D
3+12
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Solution

The correct option is A 2+13
f(x)=(x1)(x2)(x3)
f(x)=x36x2+11x6
Differentiate w.r.t. x
f(x)=3x212x+11
From f(x)=0x=12±1441326
x=2±13
Let f(x)=(xα)(xβ), α<β
and α=213, β=2+13

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.

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