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JEE Math Practice Question

Let $f(x)=\int_0^{x^2} \frac{\mathrm{t}^2-8 \mathrm{t}+15}{\mathrm{e}^{\mathrm{t}}} \mathrm{dt}, x \in \mathbf{R}$. Then the numbers of local maximum and local minimum points of $f$, respectively, are :

  1. A.3 and 2
  2. B.2 and 2
  3. C.2 and 3
  4. D.1 and 3

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