If the function f(x) defined by f(x) = x^3 - 3x + 100, (x R), (Where R is set of real numbers), then f(x) has Option 1: Local maxima at x = 1 and local minima at x = 0 Option 2: Local maxima at x = 0 and local minima at x = -1 Option 3: Local maxima at x = 1 and local minima at x = -1 Option 4: Local maxima at x = -1 and local minima at x = 1

Answer: Local maxima at x = -1 and local minima at x = 1. Solution: f'(x)=3x^2-3=0 gives x=± 1. f''(x)=6x. At x=-1, f''=-6 0, so a local minimum.

Calculus

Application of Derivatives

Easy

common

If the function $f(x)$ defined by $f(x) = x^3 - 3x + 100, (x \in \mathbb{R})$ , (Where $\mathbb{R}$ is set of real numbers), then $f(x)$ has

Local maxima at x = 1 and local minima at x = 0

Local maxima at x = 0 and local minima at x = -1

Local maxima at x = 1 and local minima at x = -1

Local maxima at x = -1 and local minima at x = 1

✅ Correct Option: 4

$f'(x)=3x^2-3=0$ gives $x=\pm 1$ .

$f''(x)=6x$ . At $x=-1$ , $f''=-6<0$ , so a local maximum; at $x=1$ , $f''=6>0$ , so a local minimum.

2026: 21 May Shift 1

Given a function $f(x) = ax + \frac{b}{x}$ ; $a > 0, b > 0$ , then

Match List-I with List-II

List-I	List-II
(A) $f(x)$ has local maxima at $x$ is equal to	(I) $\sqrt{\frac{b}{a}}$
(B) $f(x)$ has local minima at $x$ is equal to	(II) $2\sqrt{ab}$
(C) Local Maxima of $f(x)$	(III) $-\sqrt{\frac{b}{a}}$
(D) Local Minima of $f(x)$	(IV) $-2\sqrt{ab}$

Choose the correct answer from the options given below:

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The largest interval, in which the function $f(x) = x^3 + 2x^2 - 1$ is increasing, is:

If the function f(x)f(x)f(x) defined by f(x)=x3−3x+100,(x∈R)f(x) = x^3 - 3x + 100, (x \in \mathbb{R})f(x)=x3−3x+100,(x∈R), (Where R\mathbb{R}R is set of real numbers), then f(x)f(x)f(x) has

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If the function $f(x)$ defined by $f(x) = x^3 - 3x + 100, (x \in \mathbb{R})$ , (Where $\mathbb{R}$ is set of real numbers), then $f(x)$ has