JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let
\(\mathrm{f}(x)=\left\{\begin{array}{lc}3 x, & x \lt 0 \\ \min \{1+x+[x], x+2[x]\}, & 0 \leq x \leq 2 \\ 5, & x\gt2,\end{array}\right.\)
where [.] denotes greatest integer function. If \(\alpha\) and \(\beta\) are the number of points, where f is not continuous and is not differentiable, respectively, then \(\alpha+\beta\) equals __________
- A 10
- B 15
- C 5
- D 20
Answer & Solution
Correct Answer
(C) 5
Step-by-step Solution
Detailed explanation
\(f(x)=\left\{\begin{array}{ccc}3 x & ; & x 2\end{array}\right.\) \(f(x)=\left\{\begin{array}{ccc}3 x & ; & x 2\end{array}\right.\) Not continuous at \(\mathrm{x} \in\{1,2\} \Rightarrow \alpha=2\) Not diff. at \(x \in\{0,1,2\} \Rightarrow \beta=3\) \(\alpha+\beta=5\)
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