JEE Mains · Maths · STD 12 - 5. continuity and differentiation
The number of points in the interval \([2, 4]\), at which the function \(f(x) = \left[x^2 - x - \dfrac{1}{2}\right]\), where \([\cdot]\) denotes the greatest integer function, is discontinuous, is _______.
- A 2
- B 4
- C 8
- D 10
Answer & Solution
Correct Answer
(D) 10
Step-by-step Solution
Detailed explanation
Let \(g(x) = x^2 - x - \dfrac{1}{2}\). Differentiating with respect to \(x\), we get \(g'(x) = 2x - 1\). For \(x \in [2, 4]\), \(g'(x) > 0\), which implies that \(g(x)\) is strictly increasing in the interval \([2, 4]\). The values of \(g(x)\) at the endpoints are:…
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