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The function $f (x) = (x^{2} - 1) |x^{2} - 3 x + 2| + \cos (|x|)$ is not differentiable at

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answer is D.

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Detailed Solution

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

(x - 1) | x - 1 |

and cos x are differentiable for all x. But |x-2| is non-differentiable at x = 2.

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