Question

Consider the function f(x)=|x| in the interval −1≤x≤1. At the point x=0,f(x) is:

• A. (A) Continuous and differentiable
• B. (B) Non - continuous and differentiable
• C. (C) Continuous and non - differentiable
• D. (D) Neither continuous nor differentiable

Answer 1

Answer: (C)

(C) Continuous and non - differentiable

Answer 2

Explanation:
Given,f(x)=|x||x|=x for x≥0|x|=−x for x<0At x=0Left limit =0, Right limit =0,f(0)=0ASLeft limit = Right limit = Function value =0∴|x| is continuous at x=0.NowLeft derivative ( at x=0)=−1Right derivative ( at x=0)=1Left derivative ≠ Right derivative∴|x| is not differentiable at x=0Hence, the correct option is (C).