The function f(x) =

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 :

  1. four points

  2. three points

  3. two points

  4. one point


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 $x=-1 \& x=3$.

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