The function f(x)= |x^ 2 -2 x-3 | e^ |9 x^ 2 -12 x+4 | is not dif… - Vidyadip

MCQ

The function $f(x)=\left|x^{2}-2 x-3\right| \cdot e^{\left|9 x^{2}-12 x+4\right|}$ is not differentiable at exactly :

A
four points
B
three points
✓
two points
D
one point

✓

Answer

Correct option: C.

two points

c
$f(x)=|(x-3)(x+1)| \cdot e^{(3 x-2)^{2}}$

$f(x)= (x-3)(x+1) \cdot e^{(3 x-2)^{2}} ; \quad x \in(3, \infty)$

$\quad\quad\quad-(x-3)(x+1) \cdot e^{(3 x-2)^{2}} ; \quad x \in[-1,3]$

$\quad\quad\quad(x-3) \cdot(x+1) \cdot e^{(3 x-2)^{2}} \quad ; x \in(-\infty,-1)$

Clearly, non-differentiable at $x=-1\, \&\, x=3$

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