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Applications of Derivatives

If η > 1, it means the demand D is ____________ .

a) Constant function of price
b) Relatively inelastic
c) Exactly proportional to the price
d) Relatively elastic

✔Answer

Correct Answer Is : Relatively elastic

Solution Is :

If η = 1, it means the demand D is ____________ .

a) Constant function of price
b) Relatively inelastic
c) Exactly proportional to the price
d) Relatively elastic

✔Answer

Correct Answer Is : Exactly proportional to the price

Solution Is :

If 0 < η < 1, it means the demand D is ____________ .

a) Constant function of price
b) Relatively inelastic
c) Exactly proportional to the price
d) Relatively elastic

✔Answer

Correct Answer Is : Relatively inelastic

Solution Is :

Find the value of x for which the function f(x) = x³ - 6x² -15x + 1 is increasing.

a) X ∊ (5 , ∞)
b) X ∊ (- ∞, -1)
c) Both 1 and 2
d) None of these

✔Answer

Correct Answer Is : Both 1 and 2

Solution Is :

Find the value of x for which the function f(x) = 8x + (2/x) is decreasing.

a) X ∊ ((-1/2),(1/2)) - {0}
b) X ∊ ((-2),(1/2)) - {0}
c) Both 1 and 2
d) None of these

✔Answer

Correct Answer Is : X ∊ ((-1/2),(1/2)) - {0}

Solution Is :

True or false:The rate of change of the area of a circle with respect to its radius r at r = 6 cm is 8π.

a) TRUE
b) FALSE
c) Maybe
d) None of these

✔Answer

Correct Answer Is : FALSE

Solution Is :

If the function f(x) is increasing at x = c, then _________ .

a) F`( c ) > 0.
b) F`( c ) < 0.
c) F`( c ) = 0.
d) F`( c ) ≠ 0.

✔Answer

Correct Answer Is : F`( c ) > 0.

Solution Is :

If the function f(x) is decreasing at x = c, then _________ .

a) F`( c ) > 0.
b) F`( c ) < 0.
c) F`( c ) = 0.
d) F`( c ) ≠ 0.

✔Answer

Correct Answer Is : F`( c ) < 0.

Solution Is :

Demand function x, for s certain commodity is given as x = 200 - 4p, where p is the unit price. Find elasticity of demand as a function of p.

a) η = p/50
b) η = p/(50 + p)
c) η = p/(50 - p)
d) η = p/(p - 50)

✔Answer

Correct Answer Is : η = p/(50 - p)

Solution Is :

An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?

a) 900cm^ 3 / s
b) 800cm^ 3 / s
c) 700cm^ 3 / s
d) 600cm^ 3 / s

✔Answer

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Class 12 Maths Study Material

Applications of Derivatives

If η > 1, it means the demand D is ____________ .

Correct Answer Is : Relatively elastic

Solution Is :

If η = 1, it means the demand D is ____________ .

Correct Answer Is : Exactly proportional to the price

Solution Is :

If 0 < η < 1, it means the demand D is ____________ .

Correct Answer Is : Relatively inelastic

Solution Is :

Find the value of x for which the function f(x) = x 3 - 6x 2 -15x + 1 is increasing.

Correct Answer Is : Both 1 and 2

Solution Is :

Find the value of x for which the function f(x) = 8x + (2/x) is decreasing.

Correct Answer Is : X ∊ ((-1/2),(1/2)) - {0}

Solution Is :

True or false:The rate of change of the area of a circle with respect to its radius r at r = 6 cm is 8π.

Correct Answer Is : FALSE

Solution Is :

If the function f(x) is increasing at x = c, then _________ .

Correct Answer Is : F`( c ) > 0.

Solution Is :

If the function f(x) is decreasing at x = c, then _________ .

Correct Answer Is : F`( c ) < 0.

Solution Is :

Demand function x, for s certain commodity is given as x = 200 - 4p, where p is the unit price. Find elasticity of demand as a function of p.

Correct Answer Is : η = p/(50 - p)

Solution Is :

An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?

Correct Answer Is : 900cm^ 3 / s

Solution Is :

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Find the value of x for which the function f(x) = x³ - 6x² -15x + 1 is increasing.