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UPCET / UPSEE Monotonicity — practice questions

Explore 2 free Monotonicity questions in UPCET / UPSEE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Monotonicity questions and exercises with answers

Showing questions 1–2 of 2.

A function $f$ is **strictly increasing** on an interval if, on that interval:Read the answer and worked solution →If $f(x) = x^2 - 4x + 3$, the **interval** on which $f$ is decreasing is:Read the answer and worked solution →

Worked practice questions

A function $f$ is **strictly increasing** on an interval if, on that interval:

  1. $f'(x) = 0$
  2. $f'(x) > 0$
  3. $f'(x) < 0$
  4. $f'(x) = \infty$
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Correct answer: B. $f'(x) > 0$

$f'(x) > 0$ throughout an open interval ⇒ strictly increasing there. $f'(x) < 0$ ⇒ strictly decreasing. $f'(x) = 0$ at isolated points OK (e.g., $x^3$ is strictly increasing even though $f'(0) = 0$).

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If $f(x) = x^2 - 4x + 3$, the **interval** on which $f$ is decreasing is:

  1. $x < 2$
  2. $x > 2$
  3. All $x$
  4. $x = 2$
Show answer and solution

Correct answer: A. $x < 2$

$f'(x) = 2x - 4 < 0$ ⇔ $x < 2$. So $f$ is decreasing on $(-\infty, 2)$ and increasing on $(2, \infty)$. Vertex/minimum at $x = 2$.

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