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A number x makes a quadratic expression in x greatest or least: find x

The same question, asked 2 times: CDS 1 2019*, CDS 2 2024. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 1 2019

    85
    A real number xx is such that (x−x2)(x - x^2) is maximum. What is xx equal to ?

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  2. Question 2

    CDS 2 2024

    1
    A real number xx is such that the sum of the number and four times its square is the least. What is that number ?

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