f (x) = _0^x ,t ,(t , - ,1) , ,(t , - ,2) ,dt takes on its minimu… - Vidyadip

MCQ

$f (x) =$ $\int\limits_0^x {\,t\,(t\, - \,1)\,\,(t\, - \,2)\,dt} $ takes on its minimum value when:

A
$x = 0 , 1$
B
$x = 1 , 2$
✓
$x = 0 , 2$
D
$x =$$\frac{{3\,\, + \,\,\sqrt 3 }}{3}$

✓

Answer

Correct option: C.

$x = 0 , 2$

c
$f ‘ (x) = x (x - 1) (x - 2) = 0$
$x = 0, 1, $ $or$ $ 2$
at $ x = 0 \& 2,$ $ f' (x)$ changes sign from $ - ve\ to\ + ve $ $\Rightarrow $ minimum

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