We have, f(x)=(x2−9)x2−7x+12|+cos|x| ⇒f(x)=(x−3)(x+3)|(x−3)(x−4)|+cos|x| cos|x| is differentiable for all values of x ∴ We check the differentiability of (x2−9)|x2−7x+12| Let g(x)=(x2−9)|(x−3)(x−4)|
g(x)={
(x2−9)(x−3)(x−4),
x<3
−(x2−9)(x−3)(x−4),
3≤x<4
(x2−9)(x−3)(x−4),
x≥4
Clearly, g(x) is not differentiable at x=4 Hence, f(x) is not differentiable at x=4.