Question

Which of the following function is differentiable at x =0

Answer 1

Answer:

Let f(x)=sin∣x∣−∣x∣

For x<0

f(x)=−sinx+x

Derivating and putting x=0, we have

f

′

(x)=−cosx+1

f

′

(0)=−1+1=0

For x>0

f(x)=sinx−x

Derivating and putting x=0

f

′

(x)=cosx−1

f

′

(0)=1−1=0

Derivatives from both the sides are equal.

So the function is differentiable.

Hence, D is correct.