Applied Mathematics

Calculus

Medium

applied

For the function $f(x)=2x^3-21x^2+36x-5$ , which of the following statements are correct ?

A. $x=2$ is a point of local maxima.

B. $x=6$ is a point of local minima.

C. The local maximum value is 12.

D. The local maximum value is –94.

Choose the correct answer from the options given below:

A and C only

B and D only

A and D only

B and C only

✅ Correct Option: 4

$f'(x)=6(x-1)(x-6)$ , so the critical points are $x=1$ and $x=6$ .

The derivative changes from positive to negative at $x=1$ (local maximum) and from negative to positive at $x=6$ (local minimum), so A is false and B is true.

The local maximum value is $f(1)=2-21+36-5=12$ , so C is true and D is false.

2023: 30 May Shift 3

Let $f : R \to R$ be defined such that $f(x) = 16x^2 - 16x + 12$

(A) Maximum value of $f(x)$ is 8

(B) Minimum value of $f(x)$ is 8

(D) No maximum value of $f(x)$

Choose the correct answer from the options given below :

2023: 30 May Shift 3

If $C(x) = ax^2 - bx - c$ represents the total cost function then the slope of the tangent to the marginal cost curve at the point $(x, y)$ is :

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: 14 May Shift 2

The relation between 'marginal cost (MC)' and 'average cost (AC)' of producing 'x' units of a product is

2023: 7 June Shift 1

If $y = \log_3(\log_3 x)$ , then $\frac{dy}{dx}$

2023: 22 May Shift 3

If $x = 2t^2 + 3, y = 3t^2 + 6t + 5$ , then the value of $\frac{d^2y}{dx^2}$ is :

Solution

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