Applied Mathematics

Calculus

Easy

The interval in which where the function $f(x) = x^3 - 3x^2 + 4x + 1, x \in R$ is increasing in, is :

[2,3]

[-2,4]

[0,2]

✅ Correct Option: 4

$f'(x) = 3x^2 - 6x + 4 = 3(x-1)^2 + 1$ , which is always positive. So $f$ is increasing on the entire real line $R$ .

2023: 7 June Shift 1

The value of a for which the function $f(x) = a^x$ is increasing on R are given by :

2023: 22 May Shift 3

Let $f : R \to R$ be a function defined as $f(x) = 2x^3 - 21x^2 + 36x - 20$ , then :

(A) maximum value of $f(x)$ is $-3$

(B) minimum value of $f(x)$ is $-128$

(D) minimum value exists at $x = 1$

Choose the correct answer from the options given below :

2023: 30 May Shift 3

Match List - I with List - II.

List - I (Functions)	List - II (Maximum value)
(A) $f(x) = -x^2, x \in (-\infty, \infty)$	(I) 8
(B) $f(x) = -x^2 + 1, x \in (-\infty, \infty)$	(II) 7
(C) $f(x) = x + 1, x \in [0, 6]$	(III) 1
(D) $f(x) = x^3, x \in [0, 2]$	(IV) 0

Choose the correct answer from the options given below :

2026: 30 May Shift 2

Let C = C(x) be the total cost of producing x units of a product and AC is the average cost and MC is the marginal cost, then

Match List-I with List-II

List-I	List-II
(A) AC decreases with x	(I) when MC = AC
(B) AC increases with x	(II) when MC < AC
(C) AC doesn't change with x	(III) when MC = 0
(D) C is constant.	(IV) when AC < MC

Choose the correct answer from the options given below:

2023: 11 Aug Shift 1

If $C(x) = x^3 - \frac{5}{2} x^2 + 10$ represents the total cost of producing x unit by car manufacturing company. The slope of the marginal cost curve at $x = 3$ , will be

2023: 11 Aug Shift 1

the general solution of the differential equation $(1 + y) dx - 2x dy = 0$ is :

The interval in which where the function f(x)=x3−3x2+4x+1,x∈Rf(x) = x^3 - 3x^2 + 4x + 1, x \in Rf(x)=x3−3x2+4x+1,x∈R is increasing in, is :

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The interval in which where the function $f(x) = x^3 - 3x^2 + 4x + 1, x \in R$ is increasing in, is :