The number of points, where the function [f: R R], [f(x)=|x-1| |x-2| |x-1|+(x-3)|x^2-5 x+4…

Question

The number of points, where the function $$f: \mathbf{R} \rightarrow \mathbf{R}$$,

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

Accepted Answer

$$f:R \to R$$.

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

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

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

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

$$\therefore$$ Non-differentiable at $x = 1$ and $x = 4$

Solutions · 1