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Question
The function f(x) = x | x |, x ∈ R is differentiable ______.
Options
only at x = 0
only at x = 1
in R
in R – {0}
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Solution
The function f(x) = x | x |, x ∈ R is differentiable in R.
Explanation:
f(x) = x | x |, x ∈ R is differentiable.
= `{{:(x^2 ≥ 0,),(-x^2",", 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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