JEE Main 2021 (Online) 31st August Morning ShiftQuestion 1
The function $f(x)=\left|x^{2}-2x-3\right|\cdot e^{\left|9x^{2}-12x+4\right|}$ is not differentiable at exactly :
Differentiation and its Application
Solution
Concept. $9x^2-12x+4=(3x-2)^2\ge0$, so the second modulus does nothing. Corners come from $|(x-3)(x+1)|$. Formulas used. (1) $|u(x)|\,h(x)$ with $u(a)=0$, $u'(a)\ne0$, $h(a)\ne0$ has a corner at $a$Step 1 - Exponential factor. $e^{(3x-2)^2}$ is smooth and positive. Step 2 - Corners. $x^2-2x-3=(x-3)(x+1)$ has simple roots $-1$ and $3$. By (1), $f$ is not differentiable there. Step 3 - Count. Exactly two points. Answer: (B)