Question

Show that f(x) = 2x-|x| is continuous but not differentiable at x=0

Answer 1

We have f(x)=2x−∣x∣

⇒f(x)={2x−(−x)2x−(x)ifx<0ifx>0

Continuity at x=0

We have LHL as

limx→0−f(x)=limx→0−2x+x

⇒0

Step 2:

We have RHL as

limx→0+f(x)=limx→0+2x−x

⇒0

Since the LHL =RHL,the given function 2x−∣x∣ is continuous at x=0.. but not diff..