Class 12 Mathematics - Chapter Application of Derivatives NCERT Solutions | The total revenue in Rupees received fro
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.
Marginal revenue is the rate of change of total revenue with respect to the number of units sold.
\begin{align}MR=\frac{dR}{dx}\end{align}
∴Marginal Revenue
MR = 13(2x) + 26 = 26x + 26
When x = 7,
MR = 26(7) + 26 = 182 + 26 = 208
Hence, the required marginal revenue is Rs 208.
More Questions From Class 12 Mathematics - Chapter Application of Derivatives
- Q:-
The rate of change of the area of a circle with respect to its radius r at r = 6 cm is
(A) 10π (B) 12π (C) 8π (D) 11π
- Q:-
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?
- Q:- Find the rate of change of the area of a circle with respect to its radius r when
(a) r = 3 cm
(b) r = 4 cm - Q:-
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.
- Q:-
The radius of an air bubble is increasing at the rate of 1/2 cm/s. At what rate is the volume of the bubble increasing when the radius is 1 cm?
- Q:-
A balloon, which always remains spherical, has a variable diameter
\begin{align} \frac{3}{2}(2x+1)\end{align}
Find the rate of change of its volume with respect to x.
- Q:-
A balloon, which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is 10 cm.
- Q:-
A stone is dropped into a quiet lake and waves move in circles at the speed of 5 cm/s. At the instant when the radius of the circular wave is 8 cm, how fast is the enclosed area increasing?
- Q:-
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.
- Q:-
The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference?
Popular Questions of Class 12 Mathematics
- Q:-
Prove that the function f(x) = 5x – 3 is continuous at x = 0, at x = – 3 and at x = 5.
- Q:-
Determine order and degree(if defined) of differential equation \begin{align} \frac{d^4y}{dx^4}\;+\;\sin(y^m)\;=0\end{align}
- Q:-
Represent graphically a displacement of 40 km, 30° east of north.
- Q:-
If a line makes angles 90°, 135°, 45° with x, y and z-axes respectively, find its direction cosines.
- Q:-
Maximise Z = 3x + 4y
Subject to the constraints:x + y ≤ 4, x ≥ 0, y ≥ 0
- Q:-
Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis.
- Q:- Evaluate the determinants
\begin{vmatrix} \mathbf{2} & \mathbf{4} \\ \mathbf{-5} & \mathbf{-1} \end{vmatrix} - Q:- Determine whether each of the following relations are reflexive, symmetric and transitive:
(i) Relation R in the set A = {1, 2, 3,13, 14} defined as
R = {(x, y): 3x − y = 0}
(ii) Relation R in the set N of natural numbers defined as
R = {(x, y): y = x + 5 and x < 4}
(iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as
R = {(x, y): y is divisible by x}
(iv) Relation R in the set Z of all integers defined as
R = {(x, y): x − y is as integer}
(v) Relation R in the set A of human beings in a town at a particular time given by
(a) R = {(x, y): x and y work at the same place}
(b) R = {(x, y): x and y live in the same locality}
(c) R = {(x, y): x is exactly 7 cm taller than y}
(d) R = {(x, y): x is wife of y}
(e) R = {(x, y): x is father of y} - Q:-
Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P (E|F) and P(F|E).
- Q:- Integrals sin 2x
Recently Viewed Questions of Class 12 Mathematics
- Q:-
Determine order and degree(if defined) of differential y' + y =ex
- Q:-
The vertices of ΔABC are A (3, 5, −4), B (−1, 1, 2), and C (−5, −5, −2).
- Q:-
Determine order and degree(if defined) of differential equation ym + 2yn + y' =0
- Q:-
The degree of the differential equation
\begin{align}\left(\frac{d^2y}{dx^2}\right)^3\;+ \left(\frac{dy}{dx}\right)^2+\;sin\left(\frac{dy}{dx}\right)\;+ 1=\;0\end{align}
is (A) 3 (B) 2 (C) 1 (D) not defined
- Q:-
Find the direction cosines of a line which makes equal angles with the coordinate axes.
- Q:- \begin{align} \int \frac{x^3 + 3x + 4}{\sqrt{x}} . dx\end{align}
- Q:-
Let A and B be sets. Show that f : A × B → B × A such that f(a, b) = (b, a) is bijective function.
- Q:-
The order of the differential equation
\begin{align}2x^2\frac{d^2y}{dx^2}\;- \;3\frac{dy}{dx}\;+ y=\;0\end{align}
is (A) 2 (B) 1 (C) 0 (D) not defined
- Q:- \begin{align} \int \frac{x^3 + 5x^2 - 4}{x^2} . dx\end{align}
- Q:-
y = cosx + C : y' + sinx = 0
- All Chapters Of Class 12 Mathematics
- All Subjects Of Class 12