Question

The function f(x) = (x² - 1) | x² - 3x + 2 | + cos (|x|) is not differentiable at

(a) -1

(b) 0

(c) 1

(d) 2

Answer 1

Correct option (d) 2

Explanation :

The function f(x) = (x² - 1) | x² - 3x + 2 | + cos (|x|)

In differentiable of | f(x) | we hove to consider critical points for which f(x) = 0

| x | is not differentiable at x = 0

Therefore, it is differentiable at x = 0.

Therefore,

Now, x = 1,2 are critical point for differentiability.

Because f(x) is differentiable on other points in its domain.

Differentiability at x = 1

'.' Lf'(1) = Rf'(1) Therefore, function is ditlerentiable at x = 1.