QJEEM21Ma584e: JEE Main 2021 Mathematics - Class 12 JEEM21Ma584e Solution: The function is not differentiable at exactly :

Question

Verified Solution • 2025–26 Session moderate

The function

f(x) = \left| {{x^2} - 2x - 3} \right|\,.\,{e^{\left| {9{x^2} - 12x + 4} \right|}}

is not differentiable at exactly :

Accepted Answer

f(x) = \left| {(x - 3)(x + 1)} \right|\,.\,{e^{{{(3x - 2)}^2}}}

f (x) = {\begin{matrix} (x - 3) (x + 1) . e^{{(3 x - 2)}^{2}} & ; & x \in (3, \infty) \\ - (x - 3) (x + 1) . e^{{(3 x - 2)}^{2}} & ; & x \in [- 1, 3] \\ (x - 3) . (x + 1) . e^{{(3 x - 2)}^{2}} & ; & x \in (- \infty, - 1) \end{matrix}

Clearly, non-differentiable at x =

-

1 & x = 3.

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