PUCET (Punjab) Critical Points — practice questions

Explore 2 free Critical Points questions in PUCET (Punjab) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Critical Points questions and exercises with answers

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If $f(x) = x^3 - 3x$, the values of $x$ where $f'(x) = 0$ are:Read the answer and worked solution →The function $f(x) = x^3 - 3x + 1$ has critical points at:Read the answer and worked solution →

Worked practice questions

If $f(x) = x^3 - 3x$, the values of $x$ where $f'(x) = 0$ are:

$x = 0$ only
$x = 1, 0$
$x = \pm \sqrt 3$
$x = \pm 1$

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Correct answer: D. $x = \pm 1$

$f'(x) = 3x^2 - 3 = 3(x^2 - 1)$. Setting = 0: $x = \pm 1$. These are critical points (local max at $x = -1$, local min at $x = 1$).

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The function $f(x) = x^3 - 3x + 1$ has critical points at:

$x = 0, 1$
$x = \pm 1$
$x = \pm \sqrt 3$
None

Show answer and solution

Correct answer: B. $x = \pm 1$

$f'(x) = 3x^2 - 3 = 0$ ⇒ $x = \pm 1$. At $x = 1$ (local min, $f''(1) = 6 > 0$), at $x = -1$ (local max, $f''(-1) = -6 < 0$).