मराठी

The Total Cost C (X) Associated with the Production of X Units of an Item is Given by C (X) = 0.007x3 − 0.003x2 + 15x + 4000. Find the Marginal Cost When 17 Units Are Produced

Advertisements
Advertisements

प्रश्न

The total cost C (x) associated with the production of x units of an item is given by C (x) = 0.007x3 − 0.003x2 + 15x + 4000. Find the marginal cost when 17 units are produced ?

थोडक्यात उत्तर
बेरीज
Advertisements

उत्तर

Since the marginal cost is the rate of change of total cost with respect to its output, 

Marginal Cost (MC) =

\[\frac{dC}{dx}\left( x \right) = \frac{d}{dx}\left( 0 . 007 x^3 - 0 . 003 x^2 + 15x + 4000 \right) = 0 . 021 x^2 - 0 . 006x + 15\]

When x = 17,
Marginal Cost (MC) =

\[= 0 . 021 \left( 17 \right)^2 - 0 . 006(17) + 15 = 6 . 069 - 0 . 102 + 15 =\text {  Rs }20 . 967\]
shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 12: Derivative as a Rate Measurer - Exercise 13.1 [पृष्ठ ४]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
पाठ 12 Derivative as a Rate Measurer
Exercise 13.1 | Q 8 | पृष्ठ ४

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

If y = f (u) is a differential function of u and u = g(x) is a differential function of x, then prove that y = f [g(x)] is a differential function of x and `dy/dx=dy/(du) xx (du)/dx`


The length x of a rectangle is decreasing at the rate of 5 cm/minute and the width y is increasing at the rate of 4 cm/minute. When x = 8 cm and y = 6 cm, find the rates of change of (a) the perimeter, and (b) the area of the rectangle.


The total revenue in rupees received from the sale of x units of a product is given by R(x) = 13x2 + 26x + 15. Find the marginal revenue when x = 7.


The rate of change of the area of a circle with respect to its radius r at r = 6 cm is ______.


The volume of a sphere is increasing at the rate of 8 cm3/s. Find the rate at which its surface area is increasing when the radius of the sphere is 12 cm.


The volume of a sphere is increasing at the rate of 3 cubic centimeter per second. Find the rate of increase of its surface area, when the radius is 2 cm


Find the rate of change of the volume of a sphere with respect to its diameter ?


Find the rate of change of the area of a circular disc with respect to its circumference when the radius is 3 cm ?


Find the rate of change of the volume of a cone with respect to the radius of its base ?


Find the rate of change of the volume of a ball with respect to its radius r. How fast is the volume changing with respect to the radius when the radius is 2 cm?


The total revenue received from the sale of x units of a product is given by R (x) = 13x2 + 26x + 15. Find the marginal revenue when x = 7 ?


The side of a square sheet is increasing at the rate of 4 cm per minute. At what rate is the area increasing when the side is 8 cm long?


The side of a square is increasing at the rate of 0.2 cm/sec. Find the rate of increase of the perimeter of the square.


The radius of an air bubble is increasing at the rate of 0.5 cm/sec. At what rate is the volume of the bubble increasing when the radius is 1 cm?


A particle moves along the curve y = x3. Find the points on the curve at which the y-coordinate changes three times more rapidly than the x-coordinate.


The length x of a rectangle is decreasing at the rate of 5 cm/minute and the width y is increasing at the rate of 4 cm/minute. When x = 8 cm and y = 6 cm, find the rates of change of the perimeter.


The length x of a rectangle is decreasing at the rate of 5 cm/minute and the width y is increasing at the rate of 4 cm/minute. When x = 8 cm and y = 6 cm, find the rates of change of the area of the rectangle.


A circular disc of radius 3 cm is being heated. Due to expansion, its radius increases at the rate of 0.05 cm/sec. Find the rate at which its area is increasing when radius is 3.2 cm.


If \[V = \frac{4}{3}\pi r^3\] ,  at what rate in cubic units is V increasing when r = 10 and \[\frac{dr}{dt} = 0 . 01\] ?  _________________


The radius of a sphere is changing at the rate of 0.1 cm/sec. The rate of change of its surface area when the radius is 200 cm is


A cone whose height is always equal to its diameter is increasing in volume at the rate of 40 cm3/sec. At what rate is the radius increasing when its circular base area is 1 m2?


The radius of the base of a cone is increasing at the rate of 3 cm/minute and the altitude is decreasing at the rate of 4 cm/minute. The rate of change of lateral surface when the radius = 7 cm and altitude 24 cm is


The radius of a sphere is increasing at the rate of 0.2 cm/sec. The rate at which the volume of the sphere increase when radius is 15 cm, is


Each side of an equilateral triangle is increasing at the rate of 8 cm/hr. The rate of increase of its area when side is 2 cm, is


The equation of motion of a particle is s = 2t2 + sin 2t, where s is in metres and is in seconds. The velocity of the particle when its acceleration is 2 m/sec2, is


The radius of a circular plate is increasing at the rate of 0.01 cm/sec. The rate of increase of its area when the radius is 12 cm, is


The diameter of a circle is increasing at the rate of 1 cm/sec. When its radius is π, the rate of increase of its area is


In a sphere the rate of change of surface area is


A 13 m long ladder is leaning against a wall, touching the wall at a certain height from the ground level. The bottom of the ladder is pulled away from the wall, along the ground, at the rate of 2 m/s. How fast is the height on the wall decreasing when the foot of the ladder is 5 m away from the wall?


Water is dripping out at a steady rate of 1 cu cm/sec through a tiny hole at the vertex of the conical vessel, whose axis is vertical. When the slant height of water in the vessel is 4 cm, find the rate of decrease of slant height, where the vertical angle of the conical vessel is `pi/6`


A spherical ball of salt is dissolving in water in such a manner that the rate of decrease of the volume at any instant is proportional to the surface. Prove that the radius is decreasing at a constant rate


A kite is moving horizontally at a height of 151.5 meters. If the speed of kite is 10 m/s, how fast is the string being let out; when the kite is 250 m away from the boy who is flying the kite? The height of boy is 1.5 m.


If the rate of change of volume of a sphere is equal to the rate of change of its radius then the surface area of a sphere is ____________.


Let y = f(x) be a function. If the change in one quantity 'y’ varies with another quantity x, then which of the following denote the rate of change of y with respect to x.


What is the rate of change of the area of a circle with respect to its radius when, r = 3 cm


A man 1.6 m tall walks at the rate of 0.3 m/sec away from a street light that is 4 m above the ground. At what rate is the tip of his shadow moving? At what rate is his shadow lengthening?


If the circumference of circle is increasing at the constant rate, prove that rate of change of area of circle is directly proportional to its radius.


The median of an equilateral triangle is increasing at the ratio of `2sqrt(3)` cm/s. Find the rate at which its side is increasing.


A kite is being pulled down by a string that goes through a ring on the ground 8 meters away from the person pulling it. If the string is pulled in at 1 meter per second, how fast is the kite coming down when it is 15 meters high?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×