The number of real values of x at which the function f(x)= | ccc … - Vidyadip

MCQ

The number of real values of $x$ at which the function $f(x)=\left|\begin{array}{ccc}1 & |x| & x^2 \\1 & |x-1| & (x-1)^2 \\1 & |x-2| & (x-2)^2\end{array}\right|$is not differentiable is

A
$0$
B
$1$
✓
$2$
D
$3$

✓

Answer

Correct option: C.

$2$

c
(c)

$f(x)=|x-1|(x-2)^2-|x-2|(x-1)^2-|x|$

$\left(( x -2)^2-( x -1)^2\right)+ x ^2(| x -2|-| x -1|)$

$f(x)=|x-1|\left((x-2)^2-x^2\right)+|x-2|\left(x^2-\left(x^2-2 x+1\right)\right)$

$-| x |\left( x ^2-4 x +4- x ^2+2 x -1\right)$

$f ( x )=| x -1|(4-4 x )+| x -2|(2 x -1)-| x |(3-2 x )$

$f(x)=4(1-x)|1-x|+|x-2|(2 x-1)-|x|(3-2 x)$

non-derivable at $x =\frac{1}{2}$ and $x =\frac{3}{2}$

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