Advertisements
Advertisements
प्रश्न
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 ______.
पर्याय
116
96
90
126
Advertisements
उत्तर
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 126.
Explanation:
We have R (x) = 3x2 + 36x + 5
Differentiate w.r.t. x, we get
`(dR)/ dx = d/dx (3x^2 + 36x + 5) = 6x + 36`
`∴ ((dR)/dx)_(x = 15)`
`= 6 xx 15 + 36`
= 126
APPEARS IN
संबंधित प्रश्न
A point source of light is hung 30 feet directly above a straight horizontal path on which a man of 6 feet in height is walking. How fast will the man’s shadow lengthen and how fast will the tip of shadow move when he is walking away from the light at the rate of 100 ft/min.
The radius of a circle is increasing uniformly at the rate of 3 cm/s. Find the rate at which the area of the circle is increasing when the radius is 10 cm.
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?
The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference?
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 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 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 radius of a circle is increasing at the rate of 0.7 cm/sec. What is the rate of increase of its circumference?
A particle moves along the curve y = x2 + 2x. At what point(s) on the curve are the x and y coordinates of the particle changing at the same rate?
If y = 7x − x3 and x increases at the rate of 4 units per second, how fast is the slope of the curve changing when x = 2?
Find an angle θ whose rate of increase twice is twice the rate of decrease of its cosine ?
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.
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.
The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. How far is the area increasing when the side is 10 cms?
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 ?
For what values of x is the rate of increase of x3 − 5x2 + 5x + 8 is twice the rate of increase of x ?
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
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 area of a circle is equal to the rate of change of its diameter, then its radius is equal to
The equation of motion of a particle is s = 2t2 + sin 2t, where s is in metres and t is in seconds. The velocity of the particle when its acceleration is 2 m/sec2, 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 volume is
x and y are the sides of two squares such that y = x – x2. Find the rate of change of the area of second square with respect to the area of first square.
The rate of change of area of a circle with respect to its radius r at r = 6 cm is ____________.
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 ____________.
If the rate of change of the area of the circle is equal to the rate of change of its diameter then its radius is equal to ____________.
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
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?
A spherical balloon is filled with 4500π cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72π cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes after the leakage began is ______.
If a quantity \(y\) varies with another quantity \(x\) based on the rule \(y=f(x)\), which expression represents the rate of change of \(y\) with respect to \(x\)?
For a circle with area \[A=\pi r^2\], what is \[\frac{dA}{dr}\]?
When should a given value be substituted while finding a rate of change?
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?
