The function
$$f(x) = \left| {{x^2} - 2x - 3} \right|\,.\,{e^{\left| {9{x^2} - 12x + 4} \right|}}$$ is not differentiable at exactly :
Solution
$f(x) = \left| {(x - 3)(x + 1)} \right|\,.\,{e^{{{(3x - 2)}^2}}}$<br><br>$$f(x) = \left\{ {\matrix{
{(x - 3)(x + 1).\,{e^{{{(3x - 2)}^2}}}} & ; & {x \in (3,\infty )} \cr
{ - (x - 3)(x + 1).\,{e^{{{(3x - 2)}^2}}}} & ; & {x \in [ - 1,3]} \cr
{(x - 3)\,.\,(x + 1).\,{e^{{{(3x - 2)}^2}}}} & ; & {x \in ( - \infty , - 1)} \cr
} } \right.$$<br><br>Clearly, non-differentiable at x = $-$1 & x = 3.
About this question
Subject: Mathematics · Chapter: Limits, Continuity and Differentiability · Topic: Limits and Standard Results
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