JEE Main 2022 Mathematics question
Let f : be a function defined by − 3t} for x < 2; for 2 < x < 3; [x − 3] + 9 for ; 2x + 1 for x > 5, where [t] is the greatest integer less than or equal to t. Let m be the number of points where f is not differentiable and f(x)dx. Then the ordered pair (m, I) is equal to :
Answer: (3)
Solution
Let , with : g increases up to t = −1 (value 2), decreases to t = 1 and then increases, reaching g(2) = 2. So for x < 2, for x < −1 and f(x) = 2 for −1 . Then on (2, 3), 9 on [3, 4), 10 on [4, 5), 11 at x =
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