Assertion (A): Consider the function defined as f(x) = |x| + |x − 1|, x ∈ R.​ Then f(x) is not differentiable at x = 0 and x = 1.​

Question

Assertion (A): Consider the function defined as \(f(x) = |x| + |x - 1|, x \in R\). Then \(f(x)\) is not differentiable at \(x = 0\) and \(x = 1\).

Reason (R): Suppose \(f\) be defined and continuous on \((a, b)\) and \(c \in (a, b)\), then \(f(x) \) is not differentiable at \(x = c\) if \(\lim\limits_{h \to 0^-} \frac{f(c + h) - f(c)}{h} \ne \lim\limits_{h \to 0^+} \frac {f(c + h) - f(c)}h\).

(A) Both (A) and (R) are true and (R) is the correct explanation of (A).

(B) Both (A) and (R) are true but (R) is not the correct explanation of (A).

(C) (A) is true but (R) is false.

(D) (A) is false but (R) is true.

Answer 1

(A) Both (A) and (R) are true and (R) is the correct explanation of (A).