Match List - I with List - II., List - I, List - II, (A) The minimum value of f(x) = 8x^2 - 4x + 7 is, (I) 48, (B) The maximum value of f(x) = x + 1/x, x < 0 is, (II) 13, (C) The maximum slope of the curve y = -2x^3 + 6x^2 + 7x + 26 is, (III) -2, (D) The minimum value of f(x) = x^2 + 128/x is, (IV) 13/2, Choose the correct answer from the options given below : Option 1: (A)-(I), (B)-(III), (C)-(II), (D)-(IV) Option 2: (A)-(IV), (B)-(III), (C)-(II), (D)-(I) Option 3: (A)-(II), (B)-(IV), (C)-(I), (D)-(III) Option 4: (A)-(III), (B)-(IV), (C)-(II), (D)-(I)

Answer: (A)-(IV), (B)-(III), (C)-(II), (D)-(I). Solution: (A) Min at x=1/4: f = 13/2 (IV). (B) Max for x<0 at x=-1: f = -2 (III). (C) Slope max at x=1: -6+12+7 = 13 (II). (D) Min at x=4: 16+32 = 48 (I).

Applied Mathematics

Calculus

Hard

applied

Match List - I with List - II.

List - I List - II
(A) The minimum value of $f(x) = 8x^2 - 4x + 7$ is (I) 48
(B) The maximum value of $f(x) = x + \frac{1}{x}$ , $x < 0$ is (II) 13
(C) The maximum slope of the curve $y = -2x^3 + 6x^2 + 7x + 26$ is (III) $-2$
(D) The minimum value of $f(x) = x^2 + \frac{128}{x}$ is (IV) $\frac{13}{2}$

Choose the correct answer from the options given below :

List - I	List - II
(A) The minimum value of $f(x) = 8x^2 - 4x + 7$ is	(I) 48
(B) The maximum value of $f(x) = x + \frac{1}{x}$ , $x < 0$ is	(II) 13
(C) The maximum slope of the curve $y = -2x^3 + 6x^2 + 7x + 26$ is	(III) $-2$
(D) The minimum value of $f(x) = x^2 + \frac{128}{x}$ is	(IV) $\frac{13}{2}$

(A)-(I), (B)-(III), (C)-(II), (D)-(IV)

(A)-(IV), (B)-(III), (C)-(II), (D)-(I)

(A)-(II), (B)-(IV), (C)-(I), (D)-(III)

(A)-(III), (B)-(IV), (C)-(II), (D)-(I)

✅ Correct Option: 2

(A) Min at $x=1/4$ : $f = 13/2$ (IV).

(B) Max for $x<0$ at $x=-1$ : $f = -2$ (III).

(D) Min at $x=4$ : $16+32 = 48$ (I).

2023: 11 Aug Shift 1

If x is real, the minimum value of $f(x) = x^2 - 8x + 20$ is :

2026: 14 May Shift 2

The second order derivative of the function $y=\log(4x^3+6)$ with respect to 'x' will be:

2023: 23 May Shift 3

For a manufacturer, total cost function is given by $C = \frac{x^2}{25} + 2x$ . Which of the following are correct ?

A. 2.6 is the marginal cost when 5 units are produced.

B. $\frac{2x}{25} + 2$ is the marginal cost function.

C. $\frac{x}{25} + 2$ is the average cost function.

D. 2.4 is the marginal cost when 5 units are produced.

E. $\frac{x}{25} + 1$ is the average cost function.

Choose the correct answer from the options given below:

2022: 25 May Shift 1

If $y = \log_e \left(\frac{x^3}{e^3}\right)$ , then $\frac{d^2 y}{d x^2}$ is equal to

2023: 23 May Shift 3

If $y = \frac{\log x}{x^2}$ , then $\frac{d^2y}{dx^2}$ is equal to

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 :

Solution

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