The number of points, where the function f: R arrow R , f ( x )=| x -1| cos | x -2| sin | x -1| +(x-3)|x2-5 x+4|, is NOT differentiable, is:

Question

The number of points, where the function f: R arrow R , f ( x )=| x -1| cos | x -2| sin | x -1| +(x-3)|x2-5 x+4|, is NOT differentiable, is: (A) 1 (B) 2 (C) 3 (D) 4

Tardigrade Admin · Accepted Answer

f(x)=|x-1| cos |x-2| sin |x-1|+(x-3)|x2-5 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|] Non differentiable at x=1 and x=4.

Q. The number of points, where the function f:R→R,f(x)=∣x−1∣cos∣x−2∣sin∣x−1∣ +(x−3)∣∣​x2−5x+4∣∣​, is NOT differentiable, is:

1

2

3

4

f(x)=∣x−1∣cos∣x−2∣sin∣x−1∣+(x−3)∣∣​x2−5x+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∣] Non differentiable at x=1 and x=4.

Q. 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: