Calculus

Application of Derivatives

Easy

common

The function $f:R\to R$ is defined by $f(x)=2x^3+5$ , then which of the following statements are correct ?

(A) $f(x)$ has no local maximum value.

(B) $f(x)$ has no local minimum value.

(C) $f(x)$ has both local maximum and local minimum values.

(D) $f(x)$ has neither a local maximum value nor a local minimum value

Choose the correct answer from the options given below:

(A), (B) and (C) only

(A), (B) and (D) only

(B), (C) and (D) only

✅ Correct Option: 2

$f'(x)=6x^2\ge0$ , vanishing only at $x=0$ without a sign change, so $f$ is strictly increasing on $\mathbb{R}$ .

A strictly increasing function has no local extremum, so (A), (B) and (D) are true while (C) is false.

2022: 25 May Shift 1

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

2025: 30 May Shift 1

Match List-I with List-II

List-I	List-II
(A) The maximum value of $f(x) = \sin(3x) + 6$	(I) 2
(B) The maximum value of $f(x) = -\vert x + 2\vert + 4$	(II) 5
(C) The minimum value of $f(x) = (3x + 1)^2 + 5$	(III) 7
(D) The minimum value of $f(x) = 2 \cos x + 4$	(IV) 4

Choose the correct answer from the options given below:

2022: 17 Aug Shift 2

Based on above information answer the following question :

The area of the flower bed $(A(x))$ is given by :

2026: 22 May Shift 1

An angle $\theta, 0<\theta<\frac{\pi}{2}$ , which increases twice as fast as its sine, is

2022: 4 Aug Shift 1

If x is real, then minimum value of $x^2 - 8x + 17$ is :

2026: 25 May Shift 1

The rate of change of volume of a sphere with respect to its surface area when radius of the sphere is 4 cm, is

Solution