JEE Mains · Maths · STD 12 - 5. continuity and differentiation
A function \(f\) is defined on \([-3,3]\) as \(f(x)=\left\{\begin{array}{cc}\min \left\{|x|, 2-x^{2}\right\} & , \quad-2 \leq x \leq 2 \\ {[|x|]} & , \quad 2<|x| \leq 3\end{array}\right.\) where \([x]\) denotes the greatest integer \(\leq x .\) The number of points, where \(f\) is not differentiable in \((-3,3)\) is
- A \(10\)
- B \(2\)
- C \(5\)
- D \(8\)
Answer & Solution
Correct Answer
(C) \(5\)
Step-by-step Solution
Detailed explanation
\(f(x)=\left\{\begin{array}{cc}\min \left\{|x|, 2-x^{2}\right\} & , \quad-2 \leq x \leq 2 \\ {[|x|]} & , \quad 2<|x| \leq 3\end{array}\right.\) \(\Rightarrow x \in[-3,-2) \cup(2,3]\) Number of points of non-differentiability in \((-3,3)=5\)
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