Calculus

Application of Derivatives

Easy

common

The critical points of $f(x) = x^3 + x^2 + x + 1$ are

2, 1

-2, -1

2, -1

do not exist

✅ Correct Option: 4

$f'(x) = 3x^2 + 2x + 1$ . For critical points, set $f'(x)=0$ . Discriminant $= 4 - 12 = -8 < 0$ , so no real roots. Hence the critical points do not exist.

2025: 29 May Shift 2

Let $f(x) = 4x^3 - 18x^2 + 27x - 5$ , $x \in R$ . Then which of the following statements are TRUE?

(A) $f''(x) = 24x - 36$

(B) f has local maxima at $x = \frac{3}{2}$ but no minima

(D) f has both maxima and minima

Choose the correct answer from the options given below:

2026: 14 May Shift 2

In a sphere the rate of change of volume with respect to(w.r.t) time is

2022: 25 May Shift 1

The approximate volume of a cube of side a meters on increasing the side by 4% is:

2026: 30 May Shift 1

The function $f(x) = -x^3 + 12x^2 - 36x + 21$ is

A. Increasing on $(-\infty, 2)$

B. Decreasing on $(-\infty, 2)$

C. Increasing on $(2, 6)$

D. Decreasing on $(6, \infty)$

Choose the correct answer from the options given below:

2026: 19 May Shift 1

The height of a closed cylinder of given surface area and maximum volume is equal to the

2025: 13 May Shift 2

Match List-I with List-II

List-I	List-II
(A) Point of minima of $f(x) = \vert x+1\vert$	(I) 1
(B) Minimum value of $f(x) = \vert x\vert$	(II) -1
(C) Maximum value of $f(x) = 1 - x^2$	(III) 2
(D) Minimum value of $f(x) = 2 + \sin^2 x$	(IV) 0

Choose the correct answer from the options given below:

The critical points of f(x)=x3+x2+x+1f(x) = x^3 + x^2 + x + 1f(x)=x3+x2+x+1 are

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The critical points of $f(x) = x^3 + x^2 + x + 1$ are