हिंदी

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 ?

Advertisements
Advertisements

प्रश्न

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 ?

संक्षेप में उत्तर
योग
Advertisements

उत्तर

Since the marginal revenue is the rate of change of total revenue with respect to its output,
Marginal Revenue (MR) = 

\[\frac{dR}{dx}\left( x \right) = \frac{d}{dx}\left( 13 x^2 + 26x + 15 \right) = 26x + 26\]
When x = 7,
Marginal Revenue (MR)
\[= 26(7) + 26 = 182 + 26 = \text { Rs } \ 208 \]
shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 12: Derivative as a Rate Measurer - Exercise 13.1 [पृष्ठ ४]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
अध्याय 12 Derivative as a Rate Measurer
Exercise 13.1 | Q 9 | पृष्ठ ४

वीडियो ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्न

The Volume of cube is increasing at the rate of 9 cm 3/s. How fast is its surfacee area increasing when the length of an edge is 10 cm?


The rate of growth of bacteria is proportional to the number present. If, initially, there were
1000 bacteria and the number doubles in one hour, find the number of bacteria after 2½
hours. 

[Take `sqrt2` = 1.414]


The volume of a cube is increasing at the rate of 8 cm3/s. How fast is the surface area increasing when the length of an edge is 12 cm?


A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate at which the radius of the balloon increases when the radius is 15 cm.


The radius of an air bubble is increasing at the rate  `1/2`  cm/s. At what rate is the volume of the bubble increasing when the radius is 1 cm?


The total cost C(x) in rupees 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


The two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3 cm per second. How fast is the area decreasing when the two equal sides are equal to the base?


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


The total cost C(x) associated with the production of x units of an item is given by C(x) = 0.005x3 – 0.02x2 + 30x + 5000. Find the marginal cost when 3 units are produced, whereby marginal cost we mean the instantaneous rate of change of total cost at any level of output.


The radius of a circle is increasing at the rate of 0.7 cm/sec. What is the rate of increase of its circumference?


A man 2 metres high walks at a uniform speed of 5 km/hr away from a lamp-post 6 metres high. Find the rate at which the length of his shadow increases.


Find an angle θ whose rate of increase twice is twice the rate of decrease of its cosine ?


The top of a ladder 6 metres long is resting against a vertical wall on a level pavement, when the ladder begins to slide outwards. At the moment when the foot of the ladder is 4 metres from the wall, it is sliding away from the wall at the rate of 0.5 m/sec. How fast is the top-sliding downwards at this instance?
How far is the foot from the wall when it and the top are moving at the same rate?


The volume of a cube is increasing at the rate of 9 cm3/sec. How fast is the surface area increasing when the length of an edge is 10 cm?


The volume of a spherical balloon is increasing at the rate of 25 cm3/sec. Find the rate of change of its surface area at the instant when radius is 5 cm ?


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.


If a particle moves in a straight line such that the distance travelled in time t is given by s = t3 − 6t2+ 9t + 8. Find the initial velocity of the particle ?


The side of a square is increasing at the rate of 0.1 cm/sec. Find the rate of increase of its perimeter ?


The side of an equilateral triangle is increasing at the rate of \[\frac{1}{3}\] cm/sec. Find the rate of increase of its perimeter ?


A ladder, 5 metre long, standing on a horizontal floor, leans against a vertical wall. If the top of the ladder slides down wards at the rate of 10 cm/sec, then find the rate at which the angle between the floor and ladder is decreasing when lower end of ladder is 2 metres from the wall ?


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 cylindrical vessel of radius 0.5 m is filled with oil at the rate of 0.25 π m3/minute. The rate at which the surface of the oil is rising, is


The volume of a sphere is increasing at the rate of 4π cm3/sec. The rate of increase of the radius when the volume is 288 π cm3, is


A man 2 metres tall walks away from a lamp post 5 metres height at the rate of 4.8 km/hr. The rate of increase of the length of his shadow is


In a sphere the rate of change of surface area is


A cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 cubic metre per hour. Then the depth of the wheat is increasing at the rate of


Evaluate:  `int (x(1+x^2))/(1+x^4)dx`


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


If the area of a circle increases at a uniform rate, then prove that perimeter varies inversely as the radius


The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. The rate at which the area increases, when side is 10 cm is ______.


A particle is moving along the curve x = at2 + bt + c. If ac = b2, then particle would be moving with uniform ____________.


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.


A cylindrical tank of radius 10 feet is being filled with wheat at the rate of 3/4 cubic feet per minute. The then depth of the wheat is increasing at the rate of


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.


An edge of a variable cube is increasing at the rate of 10 cm/sec. How fast will the volume of the cube increase if the edge is 5 cm long? 


When \(x\) and \(y\) both vary with respect to \(t\), which formula gives the rate of change of \(y\) with respect to \(x\)?


What does a positive derivative mean for a quantity?


In calculus, which expression represents the rate of change of \(y\) with respect to \(x\) and is used in geometry, motion, business mathematics, and many real-life situations?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×