Question:
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 :
Correct Option: , 3
Solution:
$f(x)=|(x-3)(x+1)| \cdot e^{(3 x-2)^{2}}$
$f(x)= \begin{cases}(x-3)(x+1) \cdot e^{(3 x-2)^{2}} & ; \quad x \in(3, \infty) \\ -(x-3)(x+1) \cdot e^{(3 x-2)^{2}} & ; \quad x \in[-1,3] \\ (x-3) \cdot(x+1) \cdot e^{(3 x-2)^{2}} & ; \quad x \in(-\infty,-1)\end{cases}$
Clearly, non-differentiable at $x=-1 \& x=3$.