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JEE Main 2000 Mathematics question on Application of Derivatives

Let f(x)=∫ex(x−1)(x−2) dxf(x) = \int e^x(x-1)(x-2)\, dx. Then, ff decreases in the interval
  1. A.
    (−∞,−2)(-\infty, -2)
  2. B.
    (b)(b) (−2,−1)(-2, -1)
  3. C.
    (c)(c) (1,2)(1, 2)
  4. D.
    (d)(d) (2,∞)(2, \infty)
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Correct option: C

[2000]

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