JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \([t]\) denote the greatest integer less than or equal to \(\mathrm{t}\). Let \(\mathrm{f}(\mathrm{x})=\mathrm{x}-[\mathrm{x}], \mathrm{g}(\mathrm{x})=1-\mathrm{x}+[\mathrm{x}]\), and \(h(x)=\min \{f(x), g(x)\}, x \in[-2,2]\). Then \(h\) is :
- A continuous in \([-2,2]\) but not differentiable at more than four points in \((-2,2)\)
- B not continuous at exactly three points in \([-2,2]\)
- C continuous in \([-2,2]\) but not differentiable at exactly three points in \((-2,2)\)
- D not continuous at exactly four points in \([-2,2]\)
Answer & Solution
Correct Answer
(A) continuous in \([-2,2]\) but not differentiable at more than four points in \((-2,2)\)
Step-by-step Solution
Detailed explanation
\(\min \{x-[x], 1-x+[x]\}\) \(h(x)=\min \{x-[x], 1-[x-[x])\}\) \(\Rightarrow\) always continuous in \([-2,2]\) but non differentiable at \(7\) Points
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