Calculus

Application of Derivatives

Medium

core

For the function $f(x) = e^x + e^{-x}$

(A) $f'(x) = e^x - e^{-x}$

(B) The critical point is $x = 0$

(C) The minimum value is 1

(D) $x = 0$ is the point of local minimum.

Choose the correct answer from the options given below:

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

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

(A) and (D) only

✅ Correct Option: Drop

DROPPED

2026: 19 May Shift 1

For $f(x) = x^3 - 6x^2 + 9x + 15$ , which of the following statements are TRUE?

(A) $f'(x) = 3x^2 - 12x + 15$ .

(B) The critical points are 3 and 1.

(D) Local minimum value is 19.

Choose the correct answer from the options given below:

2025: 26 May Shift 2

The maximum value of the function $f(x) = x^2(60 - x)$ in [20, 80] is:

2025: 27 May Shift 1

For the function $f(x) = e^{-2x}(2-x)^2$ , the point of local maxima is:

2026: 12 May Shift 2

The maximum value of $f(x)=\dfrac{1}{3(x^2-x+1)}$ is :

2023: 23 May Shift 3

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

2025: 29 May Shift 2

Match List-I with List-II

List-I	List-II
Function f(x)	Interval for increasing/decreasing of function f(x)
---	---
(A) $f(x) = x\vert x\vert$	(I) Decreases on $(0, \infty)$
(B) $f(x) = x^2 + 2x - 5$	(II) Increases on $(3, \infty)$
(C) $f(x) = x^2 - 6x + 9$	(III) Decreases on $(-\infty, -1)$
(D) $f(x) = -x^2$	(IV) Increases on $(-\infty, \infty)$

Choose the correct answer from the options given below:

For the function f(x)=ex+e−xf(x) = e^x + e^{-x}f(x)=ex+e−x (A) f′(x)=ex−e−xf'(x) = e^x - e^{-x}f′(x)=ex−e−x (B) The critical point is x=0x = 0x=0 (C) The minimum value is 1 (D) x=0x = 0x=0 is the point of local minimum. Choose the correct answer from the options given below: