The function f(x)=x x|, x \in {\R} is differentiable:

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CBSE Class 12 Math 2023 Delhi Set 2 Solved Paper

Question : 3 of 14

Marks: +1, -0

The function f(x)=xx|,x∈R is differentiable:

only at x=0
only at x=1
in R
in R−{0}

Solution:

Explanation: f(x)=x|x|,x∈R is differentiable. ={

x2≥0

−x2,‌x<0

if x≠0,
then the function is quadratic so is differentiable.
The only point to consider is 0 . But since both x2 and −x2 have same derivative at 0 , then it follows that f is differentiable at 0 .

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