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The total cost function of a firm is C = x2 + 75x + 1600 for output x. Find the output for which the average cost ls minimum. Is CA= Cm at this output?
Concept: Derivative of Inverse Trigonometric Function
Price P for demand D is given as P = 183 +120D - 3D2 Find D for which the price is increasing
Concept: Increasing and Decreasing Functions
If x = cos2 θ and y = cot θ then find `dy/dx at θ=pi/4`
Concept: Increasing and Decreasing Functions
Find `dy/dx,if e^x+e^y=e^(x-y)`
Concept: Increasing and Decreasing Functions
Using truth table show that ∼ (p → ∼ q) ≡ p ∧ q
Concept: Increasing and Decreasing Functions
Find the marginal revenue if the average revenue is 45 and elasticity of demand is 5.
Concept: Application of Derivatives to Economics
A manufacturing company produces x items at the total cost of Rs (180 + 4x). The demand function of this product is P = (240 − x). Find x for which profit is increasing.
Concept: Application of Derivatives to Economics
Find the elasticity of demand, if the marginal revenue is 50 and price is Rs 75.
Concept: Application of Derivatives to Economics
The total cost of manufacturing x articles is C = 47x + 300x2 − x4. Find x, for which average cost is increasing.
Concept: Increasing and Decreasing Functions
Find MPC ( Marginal propensity to Consume ) and APC ( Average Propensity to Consume ) if the expenditure Ec of a person with income I is given as Ec = ( 0.0003 ) I2 + ( 0.075 ) I when I = 1000.
Concept: Increasing and Decreasing Functions
If the demand function is D = 50 - 3p - p2, find the elasticity of demand at (a) p = 5 (b) p = 2 , Interpret your result.
Concept: Increasing and Decreasing Functions
Determine the maximum and minimum value of the following function.
f(x) = `x^2 + 16/x`
Concept: Maxima and Minima
A metal wire of 36 cm length is bent to form a rectangle. Find its dimensions when its area is maximum.
Concept: Maxima and Minima
The total cost of producing x units is ₹ (x2 + 60x + 50) and the price is ₹ (180 − x) per unit. For what units is the profit maximum?
Concept: Maxima and Minima
The total cost of manufacturing x articles C = 47x + 300x2 – x4 . Find x, for which average cost is decreasing
Concept: Application of Derivatives to Economics
If the demand function is D = `((p + 6)/(p − 3))`, find the elasticity of demand at p = 4.
Concept: Application of Derivatives to Economics
For the demand function D = 100 – `p^2/2`. Find the elasticity of demand at p = 10 and comment on the results.
Concept: Application of Derivatives to Economics
Choose the correct alternative:
Slope of the normal to the curve 2x2 + 3y2 = 5 at the point (1, 1) on it is
Concept: Introduction of Derivatives
Choose the correct alternative:
The function f(x) = x3 – 3x2 + 3x – 100, x ∈ R is
Concept: Increasing and Decreasing Functions
The price P for the demand D is given as P = 183 + 120D − 3D2, then the value of D for which price is increasing, is ______.
Concept: Increasing and Decreasing Functions
