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Number of local maxima and minima of the integral from 0 to x^2 of a quadratic over an exponential

The same question, asked 2 times: 27 Jun 2022*, 22 Jan 2025. Every wording below, oldest first.

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  1. Question 1

    27 Jun 2022

    157
    If mm and nn respectively are the number of local maximum and local minimum points of the function f(x)=∫0x2t2−5t+42+etdtf(x) =\int_{0}^{x^{2}} \frac{t^{2}- 5t + 4}{2 +e^{t}}dt, then the ordered pair (m,n)(m,n) is equal to

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  2. Question 2

    22 Jan 2025

    133
    Let f(x)=∫0x2t2−8t+15etdt,x∈Rf(x) =\int_{0}^{x^{2}} \frac{t^{2}- 8t + 15}{e^{t}}dt,x \in R. Then the numbers of local maximum and local minimum points of ff, respectively, are :

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