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
(A) 116 (B) 96 (C) 90 (D) 126
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)= 3(2x) + 36 = 6x + 36
∴When x = 15,
MR = 6(15) + 36 = 90 + 36 = 126
Hence, the required marginal revenue is Rs 126.
The correct answer is D.
In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.
(i) f : R → R defined by f(x) = 3 – 4x
(ii) f : R → R defined by f(x) = 1 + x2
Show that the Modulus Function f : R → R, given by f(x) = |x|, is neither oneone nor onto, where | x | is x, if x is positive or 0 and |x| is – x, if x is negative.
Prove that the Greatest Integer Function f : R → R, given by f(x) = [x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.
In Figure, identify the following vectors.
(i) Coinitial (ii) Equal (iii) Collinear but not equal
The vertices of ΔABC are A (3, 5, −4), B (−1, 1, 2), and C (−5, −5, −2).
Represent graphically a displacement of 40 km, 30° east of north.
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
The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference?
Classify the following measures as scalars and vectors.
(i) 10 kg (ii) 2 metres north-west (iii) 40°
(iv) 40 watt (v) 10–19 coulomb (vi) 20 m/s2