AP EAMCET · Maths · Continuity and Differentiability
The set of all points where the function f (x) = 2x| x|is differentiable is
- A \((-\infty, \infty)\)
- B \((-\infty, 0) \cup(0, \infty)\)
- C \((0, \infty)\)
- D \([\infty, 0)\)
Answer & Solution
Correct Answer
(A) \((-\infty, \infty)\)
Step-by-step Solution
Detailed explanation
f(x) = 2x | x | \(f(x)=\left\{\begin{array}{cc}2 x^2 & , \quad x \geq 0 \\ -2 x^2 & , \quad x < 0\end{array}\right.\) Since, f(x) is a polynomial function, hence it will be differentiable everywhere. We need to check only at x = 0. LHD…
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