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 :
- Afour points
- Bthree points
- ✓two points
- Done point
✓
Answer
Correct option: C.
two points
c
$f(x)=|(x-3)(x+1)| \cdot e^{(3 x-2)^{2}}$
$f(x)=|(x-3)(x+1)| \cdot e^{(3 x-2)^{2}}$
$f(x)= (x-3)(x+1) \cdot e^{(3 x-2)^{2}} ; \quad x \in(3, \infty)$
$\quad\quad\quad-(x-3)(x+1) \cdot e^{(3 x-2)^{2}} ; \quad x \in[-1,3]$
$\quad\quad\quad(x-3) \cdot(x+1) \cdot e^{(3 x-2)^{2}} \quad ; x \in(-\infty,-1)$
Clearly, non-differentiable at $x=-1\, \&\, x=3$
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