Let f(x) = ∫₀^x² (t² - 8t + 15)/e^t dt, x ∈ ℝ. Then the numbers o… | JEE Main 2025 Mathematics PYQ

MCQMediumJEE Main 2025 · 22 January, Shift 2Applications of Derivatives (Monotonicity, Extrema)

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

A
$3$ and $2$
B
$2$ and $3$
C
$1$ and $3$
D
$2$ and $2$

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