QJEEM22Maa74f: JEE Main 2022 Mathematics - Class 12 JEEM22Maa74f Solution: The number of points, where the function f : R → R , f ( x ) =…

Question

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The number of points, where the function $f : R \to R$ ,

$f (x) = | x - 1 | \cos | x - 2 | \sin | x - 1 | + (x - 3) | x^{2} - 5 x + 4 |$ , is NOT differentiable, is :

Accepted Answer

$f : R \to R$ .

$f (x) = | x - 1 | \cos | x - 2 | \sin | x - 1 | + (x - 3) | x^{2} - 5 x + 4 |$

$= | x - 1 | \cos | x - 2 | \sin | x - 1 | + (x - 3) | x - 1 | | x - 4 |$

$= | x - 1 | [\cos | x - 2 | \sin | x - 1 | + (x - 3) | x - 4 |]$

Sharp edges at $x = 1$ and $x = 4$

$∴$ Non-differentiable at $x = 1$ and $x = 4$

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