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 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?


Sand is pouring from a pipe at the rate of 12 cm3/s. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm?


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


The total revenue in rupees received from the sale of x units of a product is given by R(x) = 3x2 + 36x + 5. The marginal revenue, when x = 15 is ______.


The sum of the perimeter of a circle and square is k, where k is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle.


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


A stone is dropped into a quiet lake and waves move in circles at a speed of 4 cm/sec. At the instant when the radius of the circular wave is 10 cm, how fast is the enclosed area increasing?


A man 160 cm tall, walks away from a source of light situated at the top of a pole 6 m high, at the rate of 1.1 m/sec. How fast is the length of his shadow increasing when he is 1 m away from the pole?


A man 180 cm tall walks at a rate of 2 m/sec. away, from a source of light that is 9 m above the ground. How fast is the length of his shadow increasing when he is 3 m away from the base of light?


Water is running into an inverted cone at the rate of π cubic metres per minute. The height of the cone is 10 metres, and the radius of its base is 5 m. How fast the water level is rising when the water stands 7.5 m below the base.


A kite is 120 m high and 130 m of string is out. If the kite is moving away horizontally at the rate of 52 m/sec, find the rate at which the string is being paid out.


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?


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 ?


For what values of x is the rate of increase of x3 − 5x2 + 5x + 8 is twice the rate of increase of x ?


The coordinates of the point on the ellipse 16x2 + 9y2 = 400 where the ordinate decreases at the same rate at which the abscissa increases, are


The distance moved by a particle travelling in straight line in t seconds is given by s = 45t + 11t2 − t3. The time taken by the particle to come to rest 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


If the rate of change of volume of a sphere is equal to the rate of change of its radius, then its radius is equal to


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


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 ladder 13 m long is leaning against a vertical wall. The bottom of the ladder is dragged away from the wall along the ground at the rate of 2 cm/sec. How fast is the height on the wall decreasing when the foot of the ladder is 5 m away from the wall?


For the curve y = 5x – 2x3, if x increases at the rate of 2 units/sec, then how fast is the slope of curve changing when x = 3?


Water is dripping out from a conical funnel of semi-vertical angle `pi/4` at the uniform rate of 2cm2/sec in the surface area, through a tiny hole at the vertex of the bottom. When the slant height of cone is 4 cm, find the rate of decrease of the slant height of water.


The rate of change of volume of a sphere with respect to its surface area, when the radius is 2 cm, is ______.


Two men A and B start with velocities v at the same time from the junction of two roads inclined at 45° to each other. If they travel by different roads, find the rate at which they are being seperated.


A man, 2m tall, walks at the rate of `1 2/3` m/s towards a street light which is `5 1/3`m above the ground. At what rate is the tip of his shadow moving? At what rate is the length of the shadow changing when he is `3 1/3`m from the base of the light?


The volume of a cube increases at a constant rate. Prove that the increase in its surface area varies inversely as the length of the side


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


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


The rate of change of volume of a sphere is equal to the rate of change of the radius than its radius equal to ____________.


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.


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.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×