KCET2024MathematicsContinuity and Differentiability
The function f(x)=| x| is
Options
- AEverywhere continuous and differentiable
- BEverywhere continuous but not differentiable at odd multiples of / 2
- CNeither continuous nor differentiable at (2 n+1) 2 , n Z
- DNot differentiable everywhere
Correct answer
B. Everywhere continuous but not differentiable at odd multiples of / 2
Step-by-step solution
f(x)=| x| Graph of f(x)=| x| From graph we can see that f(x) is not differentiable at points 2 , 3 2 , - 2 . . Also, it is everywhere continuous. i.e. At x=(2 n+1) 2 , n Zf(x) is not differentiable but, continuous everywhere.