PYQ Vault

Where a product with an exponential (like x^2 e^(-x)) increases or decreases

This type of question, asked 4 times: 16 May 2023 S1, 11 May 2024 S1, 21 Apr 2025 S1, 22 Apr 2025 S1. All 4 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    16 May 2023 S1

    125
    The set of all points, for which f(x)=x2e−xf(x) = x^2 e^{-x} strictly increases, is

    Tap an option to check your answer.

  2. Question 2

    11 May 2024 S1

    122
    If f(x)=xex(1−x),  x∈Rf(x) = xe^{x(1-x)},\; x \in \mathbb{R}, then f(x)f(x) is

    Tap an option to check your answer.

  3. Question 3

    21 Apr 2025 S1

    131
    The function f defined by f(x)=(x+2)e−xf(x) = (x+ 2)e^{-x} is

    Tap an option to check your answer.

  4. Question 4

    22 Apr 2025 S1

    140
    If f(x)=x⋅ex(1−x)f(x) =x\cdot e^{x(1 -x)}, then f(x)f(x) is

    Tap an option to check your answer.