The relation between 'marginal cost (MC)' and 'average cost (AC)' of producing 'x' units of a product is Option 1: d/dx(AC)=x(MC-AC) Option 2: d/dx(AC)=x(AC-MC) Option 3: d/dx(AC)=1/x(AC-MC) Option 4: d/dx(AC)=1/x(MC-AC)

Answer: d/dx(AC)=1/x(MC-AC). Solution: With total cost C(x), average cost is C/x and marginal cost is C'. Differentiating by the quotient rule: d/dx(C/x)=(xC'-C)/x^2=1/x(C'-C/x)=1/x(MC-AC).

Applied Mathematics

Calculus

Medium

applied

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

$\frac{d}{dx}(AC)=x(MC-AC)$

$\frac{d}{dx}(AC)=x(AC-MC)$

$\frac{d}{dx}(AC)=\frac{1}{x}(AC-MC)$

$\frac{d}{dx}(AC)=\frac{1}{x}(MC-AC)$

✅ Correct Option: 4

With total cost $C(x)$ , average cost is $\frac{C}{x}$ and marginal cost is $C'$ .

Differentiating by the quotient rule: $\frac{d}{dx}\left(\frac{C}{x}\right)=\frac{xC'-C}{x^2}=\frac{1}{x}\left(C'-\frac{C}{x}\right)=\frac{1}{x}(MC-AC)$ .

2023: 11 Aug Shift 1

The order and degree Of the differential equation $\frac{d^2 y}{dx^2} + 2 e^{-x} = 0$ , respectively are

2023: 22 May Shift 3

Match List - I with List - II.

	List - I		List - II
(A)	For break-even point	(I)	$< 0$
(B)	For maxima $\frac{d^2y}{dx^2}$	(II)	$\frac{dy}{dx} = 0$
(C)	For points of maxima/minima	(III)	$R(x) - C(x)$
(D)	$P(x) =$ Profit function	(IV)	$R(x) = C(x)$

Choose the correct answer from the options given below :

2023: 7 June Shift 1

A monopolist's Demand function is $x = 70 - \frac{P}{2}$ , the revenue at $x = 5$ will be :

2023: 11 Aug Shift 1

If $x = 2at, y = at^2$ , where 'a' is a constant, then $\frac{d^2 y}{dx^2}$ at $x = 2$ is :

2023: 23 May Shift 3

The total cost of producing $x$ generators is given by

TC = $x^3 - 60x^2 + 1500x + 2000$ .

The Marginal Cost (MC), when $x = 10$ units is:

2023: 15 June Shift 2

The point on the curve $y^2 = 16x$ for which the y-coordinate is changing 2 times as fast as the x-coordinate is :

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

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